Professor F. Kh. Abdullaev

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        Fatkhulla Khabibullaevich Abdullaev is a doctor of physical-mathematical sciences, a laureate of the Abu Raykhon Beruni State Prize, a honoured scientist of the Republic of Uzbekistan, and a recipient of the Al-Khorezmi medal of the Uzbek Academy for distinguished scientific achievements. Professor F. Kh. Abdullaev is an outstanding world-known scientist, who made important contributions to the development of science in the field of nonlinear physics. His works on investigation of the nonlinear dynamics of different systems in optics, laser physics, physics of condensed matter and ultra-cold quantum gases brought fame to him among the scientific community. He has created the world-recognized scientific school in the field of nonlinear physics.

        Fatkhulla Khabibullaevich Abdullaev was born on 14 January 1948 in Tashkent city, Uzbekistan. In 1964 he finished with honours the 82th school. Then he studied at the physics faculty of Tashkent State University (TSU) from 1964 to 1969. After the graduation, he served in the armed forces from year 1969 to 1971.

        In 1971 he started a post-graduate study at the Institute of Nuclear Physics (INP) of the Academy of Sciences of Republic of Uzbekistan (AS RUz) and then he was assigned to the Joint Institute on Nuclear Researches (JINR, Dubna, Russia). Here he studied the theory of weak interactions. He developed the Lie models with the non-polynomial Lagrangians and non-local interactions. He has shown that such interaction results in the existence of infinite number of ground states. He investigated the quasi-classical limit of quantum electrodynamics with gravita-tion. He has calculated a correction to the electromagnetic energy of an electron in the gravity field. Results from these works were summarized in the PhD thesis “Theory of the weak inter-actions with non-polynomial Lagrangians” defended on the joint scientific council of the AS RUz.

        After his return from the JINR, F. Kh. Abdullaev worked as a scientific researcher at the INP of the AS RUz and then as an assistant lecturer at the Theoretical Physics department of the TSU. At the same time he began to be interested in the nonlinear phenomena in different fields of physics.

        In 1977 he joined the staff of the Thermophysics Department (TPD) of the AS RUz. In 1983 he became the head of the Laboratory of wave processes at the TPD of the AS RUz.

        In 1985 he defended a thesis “Dynamics of solitons in inhomogeneous media” for the degree of doctor of science at the Scientific Council of the Institute of Theoretical Physics (Kiev, Ukraine). In the thesis, the results on the theory of solitons in condensed media have been summarized.

        From 1986 to 1992 he worked as a deputy director for science, and then as a director of the TPD of the AS RUz. During that period, he published three monographs, two of which have been translated later into English.

        In 1989 he,together with S. A. Bakhramov, S. A. Darmanyan, and M. Ya. Mesh, became a winner of the Abu Raykhon Beruni State prize for science and technology for the results on “Investigation of nonlinear wave processes of the interaction of laser radiation with matter”.

        In 1990 he received a professor academic status, and in 1995 he was awarded the rank “Honoured scientist” of Uzbekistan.

        From 1992 to 1997 he served as the head of the expert council for physics of the High Attestation Commission of the Republic of Uzbekistan.

        In recognition of his scientific achievements, in 2003 he was awarded the Al-Khorezmi medal of the AS RUz for results on the study of the Bose-Einstein condensate.

        During that period he worked on the investigation of nonlinear phenomena in optics and condensed matter, in particular, the soliton dynamics in various systems. He studied the evolution of solitons in stochastic molecular crystals, magnetics, segnetoelectrics, and liquid crystals. He investigated a chaos of nonlinear magnetic waves and of fluxons in long Josephson junctions. He has demonstrated the existence of dissipative breathers in nematic liquid crystals under simultaneous action of the viscosity and an external field. He has predicted the bound state of a proton and a domain wall in molecular chains. While studying systems, described by the Korteweg-de Vrise equation, sine-Gordon equation and nonlinear Schroedinger equation with periodic perturbations, he predicted the phenomenon of dynamical chaos of solitons, the effect that arises in non-uniform media under the action of an external field.

        The scientific work of Prof. F. Kh. Abdullaev is characterized by a quick and in-depth study of new branches of physics and by an ability to apply approaches developed in one field to the other one. He has solved the problem on the motion of a particle in the potential with the spherical symmetry under random perturbations (the stochastic Kepler problem) and has applied these results to the propagation of optical solitons in fibers with random parameters. He has created the theory of directional soliton coupler that was realized experimentally later. He has predicted the existence of an optical analogue of the Anderson localization in an array of optical fibers with random parameters. This effect was observed experimentally by the group of Prof. F. Lederer (Jena, Germany) in 2004.

        He investigated the phenomenon of modulation instability of waves in media with periodic and random variation of the parameters. The group of P. Kevrekidis from the University of Massachusetts (USA) has observed these effects in experiments in 2006. He found the new region of the modulation instability in optical fibers with the higher-order dispersion. This prediction has been confirmed in experiments of the group of G. Millot (Dijon, France) in 2003.

        Continuing the study of the soliton dynamics in inhomogeneous and random media, he applied the techniques developed in nonlinear optics to the physics of Bose-Einstein condensates (BEC). At the same time, new physical models for nonlinear fibers, optical arrays and coupled waveguides have been suggested. F. Kh. Abdullaev has developed the theory of localized modes in a Bose-condensate loaded in periodic potentials, and the theory of nonlinear excitations in a condensate under the Feshbach resonance management. He has predicted the nonlinear resonance and chaos in a condensate in a double-well potential with the varying coupling coefficient. Moreover, he has demonstrated the existence of discrete breathers in a BEC in an optical lattice. Later such breathers were observed in experiments by M. Inguscio (Florence, Italy) in 2002. In all these studies a great attention was given to the problems of the soliton stability in nonlinear optical systems, ferromagnetics, and Bose-condensates. In research on BEC, F. Kh. Abdullaev has developed the theory of the nonlinear Fresnel diffraction for matter waves. He also studied the dynamics of discrete matter wave solitons in systems with the nonlinearity management. He also has found the conditions of existence and stability of two-dimensional solitons in a condensate with the controlled dispersion. Also, the method of a generation of a soliton lattice in a BEC with the atomic scattering length slowly varying in time has been suggested. In the study of Bose-condensate in an optical lattice, he has suggested for the first time an application of the tight binding approximation, and has predicted the existence of localized modes in such a system. F. Kh. Abdullaev has developed the theory of localized modes in nonlinear lattices, including the dissipative discrete solitons in the Ablowitz-Ladik model, the nonlinear Schroedinger equation, and the Toda chain.

        Prof. F. Kh. Abdullaev is frequently invited for collaboration by leading scientific institutes and universities all over the world. Starting from 1987 he worked as a guest professor in scientific centers of Australia, United Kingdom, Germany, Brazil, Greece, Denmark, Italy, Spain, Malaysia, Portugal, USA, Finland, France, and Japan.

        Prof. F. Kh. Abdullaev places high emphasis on the education of young scientific generation. During all years, in parallel with scientific research and a supervision of members of the group, he devotes himself to teaching in universities. He has given lectures on the classical and quantum mechanics, quantum field theory, chaotic and nonlinear physics at the Physics faculty of the TSU. He was a supervisor of 12 PhD students, and a consultant of two theses for the doctor of science degree. He is a leader of the world-recognized scientific school in the field of nonlinear physics. His disciples work fruitfully in Uzbekistan and foreign countries, and many of them also became well-known specialists in this area of science.

        To date he has published about 180 scientific works in leading physical journals of the world. He has written reviews for such scientific journals like Physics reports, Progress in Optics, International Journal of Modern Physics, and regular papers in Physical Review Letters, Physical Review A, B, and E, Physics Letters, Optics Letters, Journal of the Optical Society of America, Optics Communications, Journal of Physics B, and others. Moreover, during this period he has published four monographs on important problems of modern theoretical physics.

        F. Kh. Abdullaev was an organizer of several international scientific conferences in Tashkent. He was an initiator of international conferences on nonlinear and chaotic phenomena in 1990 (“Nonlinearity and Disorder”) and in 2000 (“Nonlinearity with Disorder: Theory and Applications”) in Tashkent. He was an invited speaker in 25 scientific meetings, held in the USA, Germany, France, Spain, Portugal, Italy and Brazil. In many of these conferences he was a member of the organizing committee.

        F. Kh. Abdullaev has been awarded several times local and international grants for scientific study of fundamental problems of the nonlinear physics. For example, he has received more than ten international grants, such as grants of the CRDF, INTAS, ISF, NATO, and JSPS.

        F. Kh. Abdullaev successfully combines a talent of a researcher and a teacher. He is a genuine leader, possesses a great insight, a keenness and independence of thinking. High-level exactingness of F. Kh. Abdullaev to himself and other people goes well together with benevolent attitude to friends and colleagues. He has a great sense of humor and cheerfulness.

List of publications of Professor F. Kh. Abdullaev

Monographs

1. F. Kh. Abdullaev, P. K. Khabibullaev, Dynamics of Solitons in Inhomogeneous Condensed Media, Fan Publ., Tashkent, 1986, 200pp. (in Russian).
2. F. Kh. Abdullaev, S. A. Darmanyan and P. K. Khabibulaev, Optical solitons, Fan Publ., Tashkent, 1987, 180pp. (in Russian).
3. F. Kh. Abdullaev, Dynamical Chaos of Solitons, Fan Publ., Tashkent, 1990, 200pp. (in Russian).
4. Optical Solitons, F. Kh. Abdullaev (Ed.), World Scientific, Singapore, 1991.
5. Nonlinearity and Disorder, F. Kh. Abdullaev, A. R. Bishop, and St. Pnevmatikos (Eds.), Springer Series in Solid State, v.67, Springer-Verlag, Heidelberg, 1992.
6. Kh. Abdullaev, S. A. Darmanyan and P. K. Khabibullaev, Optical Solitons, Springer-Verlag, Heidelberg, 1993.
7. F. Kh. Abdullaev, Theory of Solitons in Inhomogeneous Media, John Wiley, Chichester, 1994.
8. Nonlinearity with Disorder: Theory and Applications, F. Kh. Abdullaev, O. Bang and M. P. Soerensen (Eds.), NATO Sience Series, vol.45, Kluwer Academic Publisher, 2001.
9. Nonlinear Waves: Classical and Quantum Aspects, F. Kh. Abdullaev and V. V. Konotop (Eds.), NATO Science Series, vol.153, Kluwer Academic Publisher, 2004.
10. F. Kh. Abdullaev, Nonlinear Matter Waves in Cold Quantum Gases, IIUM press, Kuala Lumpur, Malaysia, 2005.

Reviews

1. F. Kh. Abdullaev, Dynamical chaos of solitons and of nonlinear periodic waves, Physics Reports, v.179, n1, 1-78, 1989.
2. F. Kh. Abdullaev and S. A. Darmanyan, Chaotic dynamics of solitons and breathers, In ”Disorder and Nonlinearity”, A. R. Bishop, D. Campbell, S. Pnevmatikos (Eds.), Springer-Verlag, Heidelberg, Proc. in Physics, vol. 39, p.93, 1989.
3. F. Kh. Abdullaev, Chaotic dynamics of optical solitons, In ”Proc. Les Houshes School on Optical Solitons”, S. Wabnitz, V. E. Zakharov (Eds), Edition de Physique-Springer, 1999.
4. F. Kh. Abdullaev, S. A. Darmanyan, J. Garnier, Modulational Instability of Electromagnetic Waves in Inhomogeneous and Discrete Media, In “Progress in Optics”, E. Wolf (Ed.), Chapter 5, v.44, pp.303-365, North- Holland, Elsevier, 2002.
5. F. Kh. Abdullaev, Dynamical stabilization of nonlinear waves, In ”Nonlinear Waves: Classical and Quantum Aspects”, Kluwer Academic Publishers, Dodrecht, 2004.
6. F. Kh. Abdullaev, Discrete dissipative solitons, In “Dissipative Solitons”, N. Akhmediev and Ankiewicz (Eds.), pp.327-341, Springer-Verlag, 2005.
7. F. Kh. Abdullaev and J. Garnier, Optical solitons in random media, E. Wolf (Ed.), Progress in Optics, v.48, Chapter 2, 2005.
8. F. Kh. Abdullaev, A. Gammal, A. Kamchatnov, and L. Tomio, Dynamics of bright matter wave solitons in a Bose-Einstein condensate, Int. J. Mod. Phys. B 19, 3415 2005.
9. F. Kh. Abdullaev and J. Garnier, Bright solitons in Bose-Einstein condensates, in “Emerged Nonlinear Phenomena in Bose-Einstein Condensates”, D. Frantzeskakis, P. Kevrekidis (Eds.), Springer, 2008.

Regular articles

1. F. Kh. Abdullaev, L. Sh. Khodjaev, Lee model in the nonpolynomial quantum field theory, Preprint JINR, P2-6844, Dubna, Moscow Region, 1972.
2. F. Kh. Abdullaev, Strong gravitation and the muon mass problem, Izv. AN UzSSR, Ser. Fiz-mat. Nauk, n.2, 1972.
3. F. Kh. Abdullaev, Gravitation and finite renrmalization of the muon mass in the quantum field theory, Sov. J. Nucl. Phys. v.17, n.4, 450-41, 1973.
4. F. Kh. Abdullaev and A.Yu. Yumatov, N-theta sector of the Lee model with formfactor from the entire function class, Preprint JINR P2-7551, Dubna, Moscow Region, 1973.
5. F. Kh. Abdullaev, Regularization of weak interactions with W-bosons by the nonpolynomial lagrangians, Sov. J. Nucl. Phys., v.18, n.3, 333-335, 1974.
6. F. Kh. Abdullaev, Semileptonic and nonleptonic processes in the nonpolynomial model of weak interactions, Sov. J. Nucl. Phys., v. 19, 551-553, 1974.
7. F. Kh. Abdullaev and A. Yu.Yumatov, Physical processes in the model of weak interactions with nonpolynomial Lagrangians, preprint JINR, P2-7985, Dubna, 1974.
8. F. Kh. Abdullaev and A. Yu. Yumatov, N-theta sector of the Lee model with formfactor belonging to the class of entire functions, Theor. Math. Phys., 22, 163-166, 1975.
9. F. Kh. Abdullaev and Sh. Mutalov, Electromagnetic form-factor of neutrino in the nonlocal model of weak interactions, DAN UzSSR, n.9, 1977.
10. S. S. Abdullaev and F. Kh. Abdullaev, The definition of refraction index of diffusive waveguides by the inverse scattering method, Pisma ZhTP. v.4, 1426, 1978.
11. F. Kh. Abdullaev, Quasiclassical limit in quantum electrodynamics with gravitation, Izv. AN UzSSR, n.2, 1978.
12. S. S. Abdullaev and F. Kh. Abdullaev, On the light propagation in the system of tunnel-coupled waveguides(Anderson localization in optics), Sov.J. Radiofizika, v.23, 766 1980.
13. F. Kh. Abdullaev, Theory of nonlinear waves prpopagation in the random media, Izv.AN UzSSR, n.2, 58, 1980.
14. F. Kh. Abdullaev and I. Amirkhanov, Numerical modelling of the decoupling methods for a nonlinear stochastic equations, Preprint JINR, P11-80-269, Dubna, 1980.
15. F. Kh. Abdullaev, Soliton propagation theory in a stochastic medium with small scale fluctuations, Sov. J. Sol. State Phys. v.23, 3418-3420, 1981.
16. F. Kh. Abdullaev and A. A. Abdumalikov, Solitons in the random molecular chain, Izv.VUZ’ov SSSR, ser. Fizika, n.12, 21, 1981.
17. F. Kh. Abdullaev and B. A. Niyazov, The motion of the nonlinear Schroedinger soliton in inhomogeneous media, Zh. Tekh. Fiz., v.52, 2361-2363, 1982.
18. F. Kh. Abdullaev, Soliton-like collective excitations in stochastic molecular crystals, Theor.Mat.Phys., v.51, 607-610, 1982.
19. F. Kh. Abdullaev, Propagation of nonlinear wave in a media with fluctuating gradient of the dielectric permittivity, IZV VUZ’ov, Radiofizika, v.25, 721-722, 1982.
20. F. Kh. Abdullaev, A. A. Abdumalikov, and A. S. Rakhmatov, The dynamics of solitons in one-dimensional molecular crystals, Phys. Stat. Sol.(b), 112, K5-K10, 1982.
21. F. Kh. Abdullaev A. A. Abdumalikov, Dynamics of solitons in the disordered molecular chain, Phys. Stat. Sol.(b), 113, 685-689, 1982.
22. F. Kh. Abdullaev, Stochastic dynamics of solitons and breathers under action of random fields, Soviet PhysicsLebedev Institute Reports, n.10, 1982.
23. F. Kh. Abdullaev, Brownian motion of a soliton in the field of a regular wave packet, Soviet Physics-Lebedev Institute Reports, n.1, 52, 1983.
24. F. Kh. Abdullaev, Propagation of solitons in a random optical waveguides, Sov. J. Pisma JTPh., v.9, 306, 1983.
25. F. Kh. Abdullaev, Motion of an electron in one dimensional system with the displacement phase transition, Theor. Math.Phys. v. 56, 669-672, 1983.
26. F. Kh. Abdullaev and R. G. Djangyryan, A theory of transient radiation of the sine-Gordon soliton at intersection of interface, Zh.Tekh.Fiz. v. 53, 23077-2311, 1983.
27. F. Kh. Abdullaev and A. A. Abdumalikov, Solitons in a deformable ferromagnet, Izv. VUZ’ov, Fizika. v.11, 30, 1983.
28. F. Kh. Abdullaev, Magnetic solitons n a random ferromagnet, Fiz. Met. Mettalov. v.56, 1216, 1983.
29. F. Kh. Abdullaev, A. A. Abdumalikov, and L. Stamenkovich, Influence of thermostat on a kink dynamics in the phi-4 model. Phys. St. Sol.(b), v. 122, n1, K33-K37, 1983.
30. F. Kh. Abdullaev, Soliton motion in a random inhomogeneous molecular chain, Ukr. Fiz. Zh., v.28, 815-819, 1983.
31. F. Kh. Abdullaev and N. A. Khikmatov, The motion of a sine-Gordon soliton in a random media, Izv. VUZov-Radiofizika, 26, 295-299, 1983.
32. F. Kh. Abdullaev and A. A. Abdumalikov, Dynamics of magnetic solitons in a planar ferromagnets with random anisotropy, Phys. St. Sol.(b), v.122, K141-K146, 1984.
33. F. Kh. Abdullaev and A. A. Abdumalikov, On the damping of an elementary excitation of the quantum system interacting with a gaussian random field, Physica A 123, 625, 1984.
34. F. Kh. Abdullaev and R. Djangyryan, A theory of transient radiation of a soliton in a nonstationary medium, Radiofizika, v.27, 985-990, 1984.
35. F. Kh. Abdullaev, Influence of fluctuations on soliton dynamics in the model of structural phase transitions, Sov. J. Sol. St. Phys., v.26, 2675-2680, 1984.
36. F. Kh. Abdullaev, Dynamics of solitons under fluctuations of phonons in the quasi-one-dimensional magnets, Fiz. Met. Mettalov., v.57, 450, 1984.
37. F. Kh. Abdullaev and R. G. Djangyryan, Magnetic solitons in the anharmonic ferromagnetic crystals, Phys. St. Sol.(b), v. 129, K47-K50, 1985.
38. F. Kh. Abdullaev and N. A. Khikmatov, Dynamical chaos of bions in the long Josephson junctions, Zh. Tekh. Fiz., v.55, 937-939, 1985.
39. F. Kh. Abdullaev and B. A. Umarov, Stochastic dynamics of the Schroedinger soliton in a nonstationary medium, Izv.VUZov - Radiofizika, v.28, 664-665, 1985.
40. F. Kh. Abdullaev, S. A. Darmanyan, and B. A. Umarov, Dynamical chaos of magnetization in feromagnets under action of HF fields, Fiz. Tv. Tela (Sov.J.Sol.St.Phys.) v.27, 1620-1624, 1985.
41. F. Kh. Abdullaev, S. A. Darmanyan, and B. A. Umarov, Chaos in the parametrically driven sine-Gordon system, Phys. Lett. A, v. 108, 7-8, 1985.
42. F. Kh. Abdullaev, N. A. Khykmatov, and B. A. Umarov, Solitons dynamics in disordered systems, In ”International Symposium on selected topics instatistical mechanics”, vol.1, 11-15, D17-84-850, Dubna, Moscow Region, 1985.
43. F. Kh. Abdullaev, A. A. Abdumalikov, and P. K. Khabibullaev, Nonlinear dynamics of director of nematic in a variable magnetic field, Dokl. Akad. Nauk SSSR (Sov. Phys. Doklady), v.288, 1347-1350, 1986.
44. F. Kh. Abdullaev, N. A. Khykmatov, Distribution of KdV soliotns in the random inhomogeneous active medium, Zh. Tekh. Fiz., v.56, 1206-1207, 1986.
45. F. Kh. Abdullaev, R. M. Abrarov, and S. A. Darmanyan, Evolution of ultra-short intensive pulses in optical fibers, In ”Technology and Properties of Optical Waveguides”, Tashkent, Fan Publ., 127-136, 1986.
46. F. Kh. Abdullaev and S. A. Darmanyan, The evolution of a random field in the integrable systems. In ”Nonlinear and turbulent processes in physics”, p.12-16, Kiev, 1987.
47. F. Kh. Abdullaev, R. Gatina, and R. Djamalov, Electromagnetic modelling of the Earth in the Western Uzbekistan, Izv. AN SSS, Phys. of Earth, n.10, 109, 1987.
48. F. Kh. Abdullaev and S. A. Darnmanyan, Dynamics of random initial excitation in nonlinear one-dimensional lattice, In ”Problems of Nonlinear Acoustics”, Proc. of IUTAM Symposium on Nonlnear Acoustics, Ed. V.K.Kedrinsky, p.59-62, Novosibirsk, 1987.
49. F. Kh. Abdullaev, A. A. Abdumalikov, and E. N. Tsoi, Soliton and breather dynamics in a nematic liquid crystal, Phys. St. Sol.(b), v.146, 457- 466, 1988.
50. F. Kh. Abdullaev and A. A. Abdumalikov, Emission of electromagnetic waves by breather, Phys. St. Sol.(b), v.145, K131-K134, 1988.
51. F. Kh. Abdullaev and A. A. Abdumalikov, Propagation of soliton in a liquid crystal, Dokl. Akad. Nauk SSSR (Sov. Phys.-Doklady), v.298, 841, 1988.
52. F. Kh. Abdullaev, A. A. Abdumalikov, Interaction of solitons in coupled waveguides, Pisma Zh.Tekh.Fiz.(Sov.J.Tekh.Phys.Lett.), v.14, 1041- 1044, 1988.
53. F. Kh. Abdullaev and S. A. Darmanyan, Evolution of random pulses in a nonlinear dispersive media, Sov. J. Tekh. Phys. v.58, 265, 1988.
54. F. Kh. Abdullaev, R. M. Abrarov and S. A. Darmanyan, Dynamics of solitons in coupled optical fibers, Optics Letters, v.14, 131-134, 1989.
55. F. Kh. Abdullaev, S. A. Darmanyan, and M. R. Djumaev, Stochastic parametric resonance of solitons, Phys. Lett. A 141, 423-426, 1989.
56. F. Kh. Abdullaev and S. A. Darmanyan, Evolution of random pulses in optical fibers, Radiofizika, v.32, n.6, 1989.
57. F. Kh. Abdullaev, A. A. Abumalikov and E. N. Tsoi, Breaking of nonlinear periodic wave under the action of dissipation, In ”NonlinearWorld”, Proc. International Workshop on Nonlinear and Turbulent Processes in Physics, v.1, p.18, Kiev, 1989.
58. F. Kh. Abdullaev and B. A. Umarov, Nonlinear resonances and dynamical chaos of solitons in 3D SG system under action of a parametrically variable field, Phys. Lett. A 142, 490-492, 1989.
59. F. Kh. Abdullaev, S. A. Darmanyan, and B. A. Umarov, Chaotic dynamics of the sine-Gordon solitons under the action of periodic perturbations. In ”Solitons and applications”, V.G. Makhankov(Ed.), WS Singapore, 382386, 1989.
60. F. Kh. Abdullaev, S. A. Darmanyan, and M. R. Djumaev, Stochastic parametric resonance of solitons, In ”Solitons and applications”, V.G. Makhankov(Ed.), WS, Singapore, 327-336, 1989.
61. F. Kh. Abdullaev, A. A. Abdumalikov, and B. A. Umarov, Chaotic motion of fluxon in LJJ with periodic potential, DAN UzSSR, v.11, p.15-17, 1989.
62. F. Kh. Abdullaev, S. A. Darmanyan, and B. A. Umarov, Ulam model for the sine-Gordon soliton system, Phys.Rev. A 41, 4498-4500, 1990.
63. F. Kh. Abdullaev and S. A. Darmanyan, Dynamical chaos of domain wall motion in the ferroelectric under the action of oscillating field, Phys. St. Sol.(b), v.158, p.K201-K203, 1990.
64. F. Kh. Abdullaev, N. Flytzanis, and A. Zolotaryuk, Kink transfer of excess charge in hydrogen bounded chain, J. Mol. Electr., v.6, 75-79, 1990.
65. F. Kh. Abdullaev, A. A. Abdumalikov, and E. N. Tsoi, Nonlinear dynamics of nematics in a magnetic field. Phys.Lett. A 151, 221, 1990.
66. F. Kh. Abdullaev, A. A. Abdumalikov, and E. N. Tsoi, The nonlinear waves dynamics in nematics under the action of magnetic fields, Proc.6 Int.Workshop ”NEEDS-90”, V. G. Makhankov, A. Pashaev (Eds.), Dubna, 1990.
67. F. Kh. Abdullaev and S. A. Tadjimuratov, Influence of higher order dispersion, dissipation on soliton propagation in waveguides with the resonant impurities, Sov. Phys.-Doklady, 316, n2, 1991.
68. F. Kh. Abdullaev and A. A. Abdumalikov, Chaotic dynamics of nonlinear Schroedinger soliton, interacting with oscillating impurity, Phys. St. Sol.(b), 167, 503, 1991.
69. F. Kh. Abdullaev and B. A. Umarov. In ”Coherent Structures in Physics and Biology”, M.Remoissenet, M. Peyrard (Eds), Springer-Verlag, v.60, 1991.
70. F. Kh. Abdullaev, B. A. Umarov. Stochastic dynamics of a spatial soliton on the periodic interface of two nonlinear media. Phys. Lett. A 160, 429-432, 1991.
71. F. Kh. Abdullaev, S. A. Darmanyan. Solitons in system of coupled and inhomogeneous waveguieds. Proceedings of the workshop on optical solitons. Tashkent, 1989. World Scientific. 1991, p.3-12.
72. F. Kh. Abdullaev, S. A. Darmanyan, P. Bussimer. Propagation of solitons through interface in optical fiber. Ibid. p.13-20. 1991.
73. F. Kh. Abdullaev, R. M. Abrarov, S. A. Darmanyan, V. Goncharov. Soliton switching in the dualcore active coupler. Letters in Soviet J. Techn. Phys. v.18, n.14, 1992.
74. F. Kh. Abdullaev, B. A. Umarov. Chaotic dynamics of fluxons in a large area Josephson junctions. In ”Physics in two dimension R. Morf (Ed), Helv. Phys. Acta, 65, n2/3, 494-496, 1992.
75. F. Kh. Abdullaev, A. A. Abdumalikov, B. A. Umarov. Dynamics of solitons in segnetomagnets with the easy plane magnetic anisotropy. Phys. Lett. A 171 125-128, 1992.
76. F. Kh. Abdullaev, A. A. Abdumalikov, B. A. Umarov. Dynamics of solitons in segnetomagnets. Ukrain. Phys. Journ., 37, n.12, 1846-1850, 1992.
77. F. Kh. Abdullaev, R. Gulyamov. Theory of nonlinear coupler with the resonant impurities. Pisma Zh. Tekh. Fiz.(JTP Letters.), 18, No.20, 10-13, 1992.
78. F. Kh. Abdullaev, A. A. Abdumalikov, E. N. Tsoi. Stability of solitons and nonlinear periodic waves in a liquid crystal. Phys. Lett. A 174, 403-406, 1993.
79. F. Kh. Abdullaev. Nonlinear resonances and chaos in periodically modulated Fabry-Perot etalon. Uzbek Phys. Journ. n.2, 76, 1993.
80. F. Kh. Abdullaev, S. A. Darmanyan, P. L. Christiansen, M. Soerensen. Modulational instability of electromagnetic waves in optical fibers near the zero dispersion point. Opt. Commun. 108, n.1, 60-64, 1994.
81. F. Kh. Abdullaev, J. G. Caputo, N. Flytzanis. Envelope soliton propagation in media with temporally modulated dispersion. Phys. Rev. E 50, n2, 1552-58, 1994.
82. F. Kh. Abdullaev. Modulational instability of electromagnetic waves in bers with periodically modulated parameters. Pisma Zh. Tekh. Fiz.(JTP Letters), v. 20, 63-66, 1994.
83. F. Kh. Abdullaev, R. M. Abrarov, S. A. Darmanyan, B. Goncharov. Solitons interaction in nonlinear directional coupler. Techn. Phys. 39, N9, p.916, 1994.
84. F. Kh. Abdullaev, B. B. Baizakov, B. Umarov. Propagation of chirped optical pulses in the fibers with random dispersion, Pisma Zh. Tekh. Fiz.( JTP Letters), 20, 29-33, 1994.
85. F. Kh. Abdullaev. Interaction of a spatial soliton with modulated interface, ESF Study Center, Abstract of talks, p.1, Edinburgh 1994.
86. F. Kh. Abdullaev, S. Tadjimuratov. Interaction of dark soliton with periodic wave in optical waveguides. Opt.Commun. 116, n2, p.179-182, 1995.
87. F. Kh. Abdullaev. Envelope solitons in the media with modulated dispersion. In ”Fluctuation phenomena:Nonlinearity and Disorder”. A. R. Bishop, L. S.Vazquez (Eds), Madrid, World Scientific, 1995, p.365-372.
88. F. Kh. Abdullaev, S. A. Darmanyan, M. R. Djumaev, A. Majid, M. P. Soerensen, Evolution of randomly modulated soliton in the KdV equation, Phys. Rev.E 52, n.10, 3577-83, 1995.
89. F. Kh. Abdullaev, M.R. Djumaev. Evolution of random initial fields in a nearintegrable systems. J. Techn. Phys., 65, n.8, p.1-10, 1995.
90. F. Kh. Abdullaev, R. M. Abrarov, S. A. Darmanyan, V. Goncharov. Self-localization Phenomenon and Influence of Raman Self-Scattering on the Dynamics of Femtosecond Solitons. In ”Studies in Classical and Quantum Nonlinear Optics”, Editor O. Keller. Nova Science, Publ. Inc., New York, 1995.
91. F. Kh. Abdullaev, J. G. Caputo, N. Flytzanis. Evolution of envelope soliton in a modu-lated and random media. Proc.XI-th Inter. Congress in Math.Phys.,Ed. D. Jagolnitzer, Int. Press, Cambridge, p.761, 1995.
92. F. Kh. Abdullaev, B. B. Baizakov, B. A. Umarov. Distortion of nonlinear periodic wave on random interface. JTP Letters, 21, n.14, p. 1995.
93. F. Kh. Abdullaev. Stochastic instability of chirped soliton in the fiber with periodically varying parameters. In ”Physics and Applications of Optical Solitons in Fibres’95. A. Hasegawa (Ed), Kluwer Publishers, N.Y.,p.89-98, 1996.
94. F. Kh. Abdullaev, S. A. Darmanyan, A. Kobyakov, F. Lederer. Modulational instability of electromagnetic waves in optical bers with variable dispersion, Phys.Lett. A 220, n.4-5, 213-218, 1996.
95. F. Kh. Abdullaev, S. A. Darmanyan, F. Lederer, Evolution of randomly perturbed pulses in optical fibers. Opt. Commun., 126, 89-94, 1996.
96. F. Kh. Abdullaev, A. Kirakosyan. 2D local modes and vortices in the anysotropic ferromagnets, Preprint ICTP, Trieste, 1996.
97. F. Kh. Abdullaev, S. A. Darmanyan, S. Bishoff, M.P. Soerensen. Modulational instability in the extended nonlinear Schrodinger equation with varying nonlinearity, J. Opt. Soc. Am., B 14, 27-33, 1997.
98. F. Kh. Abdullaev, A. A. Abdumalikov, B. Baizakov. Stochastic in stability of chirped pulses in media with periodic gain. Kvant. Elektron., 24, n.2, 176-180, 1997.
99. F. Kh. Abdullaev, A. A. Abdumalikov, B. B. Baizakov.Propagation of chirped optical soliton in fiber with random parameters. Opt. Commun., 138, 49-54, 1997.
100. F. Kh. Abdullaev, E. N. Tsoy. Chaotic dynamics of fluxon in the inhomogeneous long Josephson junction, J. Techn. Phys., 40, n.5, 1997.
101. F. Kh. Abdullaev, J. G. Caputo. Propagation of envelope soliton in media with varying spatial dispersion, Phys. Rev. E 55, 6061-71, 1997.
102. F. Kh. Abdullaev. Modulational instability of electromagnetic waves in the long Josephson junctions, Tech. Phys. Lett, 23, p.52-53, 1997.
103. F. Kh. Abdullaev, N. Nurmanov, E. N. Tsoy, Variational approach to the problem of dark-soliton generation, Phys. Rev. E 56, n.3, pp.3638-3644, 1997.
104. F. Kh. Abdullaev. Spatial soliton propagation in array of planar nonlinear waveguides with a periodically varying tunnel-coupling, J. Techn. Phys., v.68, 1, 1998.
105. F. Kh. Abdullaev, D. Navotny, B. A. Umarov. Influence of thermal fluctuations on bi-solitonic state dynamics in the stacked long Josephson junctions, Phys. Lett. A 244, 155-159, 1998.
106. F. Kh. Abdullaev, A. A. Abdumalikov. Evolution of randomly perturbed sine-Gordon kink , Physica D v.113, 115 (1998).
107. F. Kh. Abdullaev, J. G. Caputo, and M. P. Soerensen, Propagation and interaction of optical solitons in fibers with random parameters, In ”New trends in Optical Solitons in Fibers”, Ed. A.Hasegawa, Kluwer, Dodrecht, 1998 .
108. F. Kh. Abdullaev, B. B. Baizakov, B. A. Umarov, Resonant phenomena in interaction of a spatial soliton with the modulated interface of two nonlinear media, Opt .Comm., v.156, 341-346, 1998.
109. F. Kh. Abdullaev, S. Bishoff, H. Hansen, M. P. Soerensen, and J. Smeltnik. Propagation and interaction of optical solitons in random media, J. Opt. Soc. Am. B 15, n.9, 2424, 1998.
110. F. Kh. Abdullaev and J. G. Caputo. Validation of the variational approach for chirped pulses in fibers with periodic dispersion, Phys. Rev. E 58, n.5, p.6637, 1998.
111. B. A. Umarov, F. Abdullaev, and M. R. Wahiddin. Soliton interaction and switching in a coupler with third order dispersion and the Raman effect, Opt.Comm. 162, 340, 1999.
112. F. Kh. Abdullaev, J. Garnier, Modulational instability of electromag netic waves in birefringent bers with a periodic and random dispersion, Phys. Rev. E 60, 6657, 1999.
113. E. Tsoy, I. Stewart, and F. Kh. Abdullaev, Soliton switching in smectic C* liquid crystals, Phys. Rev. E 60, n.5, pp.5568-5574, 1999.
114. F. Kh. Abdullaev, R. Galimzyanov, and A. Kirakosyan, Dynamics of vortices in 2D ferromagnets with an easy axes anysotropy, Phys.Rev., B 60, n.9, 6590, 1999.
115. F. Kh. Abdullaev, S. A. Darmanyan, A. Kobyakov, V. Schmidt, and F. Lederer. Evolution of solitons in quadratic media with fluctuating parameters, Opt.Commun., 168, pp.213-218, 1999.
116. F. Kh. Abdullaev, J. Garnier , Propagation of soliton in media with random dispersive perturbations, Physica D 134, pp. 303-315, 1999.
117. F. Kh. Abdullaev, J. C. Bronski and G. C. Papanicolaou, Solitons under perturbations-random Kepler problem, Physica D 135, n.3-4, pp.369-386, 2000.
118. F. Kh. Abdullaev, B. B. Baizakov, Disintegration of optical soliton in fiber lines with random dispersion map, Opt. Lett., 25, pp.93-95, 2000.
119. F. Kh. Abdullaev, B.Baizakov, B. Umarov, D. Navotny, Tolerance of the optical solitons to random variations of dispersion map, In ”Massive WDMand TDM solitonic communication systems, A. Hasegawa (Ed.), Kyoto Conference Proceedings, Kluwer, Dodrecht, 2000.
120. F. Kh. Abdullaev, A. A. Abdumalikov. Evolution of a randomly modulated breather, J. Techn. Phys., 70, n.6, pp.16-19, 2000.
121. F. Kh. Abdullaev, M. R. Djumaev, E. N. Tsoy. Distribution function of fluxons in the long Josephson junction with random current, J. Techn. Phys., 70, n5, pp.43-47, 2000.
122. A. Gammal, L. Tomio, F.Kh. Abdullaev, Stability of the Bose- Einstein condensate with two and three body interactions, Phys.Lett. A 267, 305-311, 2000.
123. F .Kh. Abdullaev, B. A. Umarov, M. R. Wahiddin and D. Navotny, Dispersion-managed solitons in a periodically and randomly inhomogeneous birefringent optical fiber, J. Opt. Soc. Am. B 17, n.7,1117-1124, 2000.
124. F. Kh. Abdullaev, R. A. Kraenkel, Macroscopic quantum tunneling in coupled Bose-Einstein condensates with time dependent trap, Phys.Rev. A 62, 023613, 2000.
125. J. Garnier and F. Kh. Abdullaev, Modulational instability in nonlinear Schroedinger equation with random parameters, Physica D 145, pp.65-83, 2000.
126. F. Kh. Abdullaev, A. Abdumalikov(jr), L. Boisson, and E. N. Tsoy, Phase-locked solutions of a capacitevely coupled Josephson junctions, Phys. Rev. B 62, n.10, pp.6766-6773, 2000.
127. F. Kh. Abdullaev, R. A. Kraenkel, Macroscopic quantum tunneling and resonances in coupled Bose-Einstein condensates with oscillating atomic scattering length, Phys.Lett., A 272, pp.395-401, 2000.
128. F. Kh. Abdullaev, A. Gammal, L. Tomio, T. Frederico, Stability of trapped Bose-Einstein condensates, Phys. Rev. A 63, 043604, 2001.
129. V. Filho, F. Kh. Abdullaev, A. Gammal, L. Tomio, Autosolitons in the Bose-Einstein condensate with two and three body relaxations, Phys. Rev. A 63, 053603, 2001.
130. J. Garnier, F. Kh. Abdullaev, E. Seve, and S. Wabnitz, Role of polarization mode dispersion on modulational instability in optical fibers, Phys. Rev., E 63, 066616, 2001.
131. E. N. Tsoy, M. Sterke, F. Kh. Abdullaev Two-photon absorption and modulational instabilities in fibers, J. Opt. Soc. Am. B 18, 1144, 2001.
132. F. Kh. Abdullaev, B. B. Baizakov, V. V. Konotop, Dynamics of Bose-Einstein Condensate in Optical Trap, In ”Nonlinearity and Disorder:Theory and Applications”, Eds. F. Kh. Abdullaev, O. Bang, and M. P. Soerensen, Kluwer AP, 2001.
133. A. Kobyakov, F. Kh. Abdullaev, S. A. Darmanyan, E. Schmidt, F. Lederer, Spatial solitons in random quadratic media, In ”Nonlinearity and Disorder; Theory and Applications”, Eds. F. Kh. Abdullaev, O. Bang, and M. P. Soerensen, Kluwer AP, 2001.
134. F. Kh. Abdullaev, B. B. Baizakov, S. A. Darmanyan and V. V. Konotop, M. Salerno, Nonlinear excitations in arrays of Bose-Einstein condensates, Phys. Rev. A 64 , n.4, 043606, 2001.
135. F. Kh. Abdullaev, E. N. Tsoy, Evolution of two beams in a focusing medium, Physica D 161, 67, 2002.
136. A. Kirakosyan, F. Kh. Abdullaev, and R. Galimzyanov, Bloch walls in strongly driven easy plane ferromagnets, Phys.Rev. B 65, 094411, 2002.
137. F. Kh. Abdullaev, D. V. Navotny, Dispersion-managed solitons in fibers with random dispersion, Technical Physics Letters, 28, 942-944, 2002.
138. F. Kh. Abdullaev, A. A. Abdumalikov and B. A. Umarov, Autosoliton in Ablowitz-Ladik chain with linear damping and nonlinear amplification, Phys. Lett. A 305/6, 371-376, 2002.
139. F. Kh. Abdullaev, Jean Guy Caputo, Roberto Kraenkel, Boris Malomed, Controllable dynamics of BEC with varying atomic scattering length, Phys.Rev. A 67, 013606, 2003.
140. J. Garnier, F. Kh. Abdullaev, Soliton dynamics in a random Toda chain, Phys.Rev. E 67, 026609, 2003.
141. J. Garnier, F. Kh. Abdullaev, A statistical approach of the decay of a soliton in a randomly perturbed Toda chain, JHEP, Proceedings, 2003.
142. F. Kh. Abdullaev, J.C. Bronski, R. Galimzyanov, Dynamics of 2D Bose-Einstein condensate with time-varying atomic scattering length, Physica D 184/1-4, 319-332, 2003.
143. F. Kh. Abdullaev, R. Galimzyanov, Dynamics of bright matter wave solitons in a quasi 1D Bose-Einstein condensate with a rapidly varying trap, J. of Physics , B 36, 1099, 2003.
144. E. N. Tsoy, F. Kh. Abdullaev, Interaction of pulses in nonlinear Schroedinger model, Phys. Rev. E 67, 056610, 2003.
145. F. Kh. Abdullaev, A.M. Kamchatnov, V.V. Konotop and V. Brazhnii, Adiabatic evolution of periodic waves in Bose-Einstein condensate, Phys. Rev. Lett., 90, 0230402, 2003.
146. F. Kh. Abdullaev, V. V. Konotop, Intrinsic localized modes in array of atom-molecular Bose-Einstein condensates, Phys. Rev. A 68, n1, 013605 2003.
147. F. Kh. Abdullaev and M. Salerno, Adiabatic compression of soliton matter waves, J. Phys. B 36, 2851, 2003.
148. F. Kh. Abdullaev, B. B. Baizakov and M. Salerno, Stable two dimensional dispersion-managed soliton, Phys. Rev. E 68, 066605 (2003).
149. F. Kh. Abdullaev, E. N. Tsoy, B. A. Malomed and R. A. Kraenkel, An array of Bose-Einstein condensates under time-periodic Feshbach resonances management, Phys. Rev. A 68, 053606 (2003).
150. A. Kamchatnov, A. Gammal, F. Kh. Abdullaev and R. Kraenkel, Formation of soliton trains in Bose-Einstein condensate as a nonlinear Fresnel diffraction of matter waves, Phys. Lett. A 319, 406-412, (2003).
151. F. Kh. Abdullaev, E. N. Tsoy, B. A. Malomed and R. A. Kraenkel, Discrete solitons in the array with variable scattering length, In ”Nonlinear Waves:Classical and Quantum aspects, Kluwer Academic Publishers, Dodrecht, (2004).
152. F. Kh. Abdullaev, D. Navotny, and B. B. Baizakov, Optical pulse propagation in fibers with random dispersion, Physica D 192, 83-94, (2004).
153. F. Kh. Abdullaev, A. Gammal and L. Tomio, Dynamics of bright matter waves solitons in Bose-Einstein condensate with inhomogeneous scattering length, J. Phys. B 37, 1-17, (2004).
154. J. Garnier, F. Kh. Abdullaev, and B. B. Baizakov, Collapse of the Bose-Einstein condensate by fluctuations of the laser intensity, Phys. Rev. A 69, 053607 (2004).
155. F. Kh. Abdullaev, R. A. Kraenkel and B.A. Umarov, Quantum Coherent Tunnelling between two Atomic-Molecular Bose-Einstein Condensates Europ. J. Phys. D 30, 369 (2004).
156. F. Kh. Abdullaev, R. G. Galimzyanov, M. Brtka, and R. A. Kraenkel, Nonlinear oscillations of 3D BEC under periodically varying atomic scattering length, J. Phys. B 37, 3535-3550 (2004).
157. F. Kh.Abdullaev and J. Garnier, Collective oscillations of one-dimensional Bose-Einstein gas under varying in time trap potential and atomic scattering length, Phys. Rev. A 70, 053604, (2004).
158. F. Kh. Abdullaev, J. G. Caputo, B. A. Malomed and R. A. Kraenkel, J. Low. Temp. Phys. 134, 671 (2004).
159. D. Mihaelis, F. Kh. Abdullaev, S. A. Darmanyan, and F. Lederer, Ising-Bloch transition for the parametric Ginzburg-Landau equation with rapidly varying perturbations, Phys. Rev. E 71, 056205 (2005).
160. J. Garnier and F. Kh. Abdullaev, Symmetry breaking induced by random fluctuations for Bose-Einstein condensates in a double-well trap, Phys. Rev. E 71, 033603 (2005).
161. F. Kh. Abdullaev, S. Jesni, and M. R. Wahiddin, Coupled mode theory for BEC’s with varying nonlinearity, Phys. Lett. A 345, 247 (2005).
162. F. Kh. Abdullaev and M. Salerno, Gap-Townes solitons and localized excitations of low dimensional Bose-Einstein condensates in optical lattices, Phys. Rev. A 72, 033617 (2005).
163. F. Kh. Abdullaev and J. Garnier, Cubic-quintic nonlinear Schroedinger model with nonlinear management, Phys. Rev. E 72, 035603 (2005).
164. F. Kh. Abdullaev, V. Filho, A. Gammal, and L. Tomio, Bose-Einstein condensate with inhomogeneous scattering length in one and two dimensions, Physics of Particles and Nuclei, Vol. 36, Suppl.2, pp.S213-216 (2005).
165. V. Barros, M.Brtka, A.Gammal, and F. Kh. Abdullaev, Solitons interaction in BC with harmonic trap potential, J. Phys. B 38, 4111 (2005).
166. F. Kh. Abdullaev and J. Garnier, Propagation of matter wave solitons in periodic and random nonlinear potentials, Phys. Rev. A. 72, 061605(R) (2005).
167. F. Kh. Abdullaev, R. M. Galimzyanov, and Kh. Ismatullaev, Collective oscillations of a quasi one dimensional Bose gas under damping, Phys. Lett. A 357, 48 (2006).
168. F. Kh. Abdullaev and J. Garnier, Transmission of matter wave solitons through nonlinear traps and barriers, Phys. Rev. A, 74, 013604 (2006).
169. J. Garnier, F. Kh. Abdullaev, and M. Salerno, Solitons in strongly driven discrete nonlinear Schroedinger - type models, Phys. Rev. E 75, 016615 (2007).
170. F. Kh. Abdullaev and J. Garnier, Dynamical localization of matter wave solitons in managed barrier potentials, Phys. Rev. A 75, n2, 033603 (2007).
171. F. Kh. Abdullaev, A. A. Abdumalikov, and R. M. Galimzyanov, Gap solitons in Bose-Einstein condensates in linear-nonlinear optical lattices, Phys. Lett. A 367, 149 (2007).
172. F. Kh. Abdullaev, A. Bouketir, A. Messikh, and B. A. Umarov, Discrete breathers in Bose-Einstein condensates with three body interactions in optical lattice, Physica D 232, 54 (2007).
173. F. Kh. Abdullaev, A. Gammal, H. Luz, and L. Tomio, Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice, Phys. Rev. A 76, 043611 (2007).
174. F. Kh. Abdullaev, Yu. A. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, Generalized neighbor-interaction models induced by nonlinear lattices, Phys. Rev. E, v.76 1 (2007).
175. F. Kh. Abdullaev, R. M. Galimzyanov, and H. Ismattullaev, Collective excitations of a BEC under anharmonic trap position jittering, J. Phys. B, v.41, 015301 (2007).