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Theory of Optical Bullets
By
, Vol. 36, 21-59, 2002
Abstract
This paper is a theoretical study of solitons in multidimensions, also known as optical bullets, that is governed by the nonlinear Schrodinger's equation in 1 + 3 dimensions. The parameter dynamics of such multidimensional solitons has been obtained. The study is extended to obtain the adiabatic evolution of soliton parameters in presence of the perturbation terms. Furthermore, the parameter dynamics for the vector multidimensional solitons and including the presence of the perturbation terms has been obtained.
Citation
"Theory of Optical Bullets," , Vol. 36, 21-59, 2002.
doi:10.2528/PIER01110502
References

1. Abdullaev, F., S. Darmanyan, and P. Khabibullaev, Optical Solitons, Springer Verlag, New York, 1993.

2. Ablowitz, M. J. and H. Segur, Solitons and the Inverse Scattering Transform, SIAM, Philadelphia, USA, 1981.

3. Ablowitz, M. J., G. Biondini, and S. Blair, "Localized multidimensional optical pulses in non-resonant quadratic materials," Mathematics and Computers in Simulation, Vol. 56, No. 6, 511-519, 2001.

4. Afanasjev, V. V., P. L. Chu, and Y. S. Kivshar, "Breathing spatial solitons in non-Kerr media," Optics Letters.

5. Akhmediev, N. N., V. I. Korneev, and R. F. Nabiev, "Modulation instability of the ground state of the nonlinear wave equation: optical machine gun," Optics Letters, Vol. 15, 393-395, 1992.

6. Akhmediev, N. N. and J. M. Soto-Crespo, "Generation of a train of three-dimensional nonlinear Schrodinger equation," Physical Review A, Vol. 47, No. 2, 1358-1364, 1993.

7. Akhmediev, N. N. and A. Ankiewicz, Solitons Nonlinear Pulses and Beams, Chapman and Hall, UK, 1997.

8. Akhmediev, N. N., A. Ankiewicz, and R. Grimshaw, "Hamiltonian-versus-energy diagrams in soliton theory," Physical Review E, Vol. 59, No. 5, 6088-6096, 1999.

9. Akhmediev, N. N., "Spatial solitons in Kerr and Kerr-like media," Optical and Quantum Electronics, Vol. 30, 535-569, 1998.

10. Bang, O., J. J. Rasmussen, and P. L. Christiansen, "Subcritical localization in the discrete nonlinear Schr¨odinger equation with arbitrary power nonlinearity," Nonlinearity, Vol. 7, No. 1, 205-218, 1994.

11. Biswas, A., "Perturbation of solitons due to power law nonlinearity," Chaos, Solitons and Fractals, Vol. 12, No. 3, 579-588, 2001.

12. Biswas, A., "Solitons in multiple-core couplers," Journal of Nonlinear Optical Physics and Materials, Vol. 10, No. 3, 2001.

13. Biswas, A., "Solitons in nonlinear fiber arrays," Journal of Electromagnetic Waves and Applications, Vol. 15, No. 9, 1189-1196, 2001.

14. Biswas, A., "Perturbation of solitons with non-Kerr law nonlinearity," Chaos, Solitons and Fractals, Vol. 13, No. 4, 815-823, 2002.

15. Blagoeva, A. B., S. G. Dinev, A. A. Dreischuh, and A. Naidenov, "Light bullets formation in a bulk media," IEEE Journal of Quantum Electronics, Vol. 27, 2060-2062, 1991.

16. Busalev, V. S. and V. E. Grikurov, "Simulation of instability of bright solitons for NLS with saturating nonlinearity," Mathematics and Computers in Simulation, Vol. 56, No. 6, 539-546, 2001.

17. Desyatnikov, A., A. Maimistov, and B. Malomed, "Three dimensional spinning solitonsin dispersive media with cubicquintic nonlinearity," Physical Review E, Vol. 61, No. 3, 3107-3113, 2000.

18. Emundson, D. E. and R. H. Enns, "The particle-like nature of colliding light bullets," Physical Review A, Vol. 51, No. 3, 2491-2498, 1995.

19. Emundson, D. E. and R. H. Enns, "Bistable light bullets," Optics Letters, Vol. 17, 586-588, 1992.

20. Enns, R. H. and D. E. Emundson, "Guide to fabricating bistablesoliton-supporting media," Physical Review A, Vol. 47, No. 5, 4524-4527, 1993.

21. Enns, R. H. and S. S. Rangnekar, "Bistable spheroidal optical solitons," Physical Review A, Vol. 45, No. 5, 3354-3357, 1992.

22. Enns, R. H. and S. S. Rangnekar, "Variational approach to bistable solitary waves in d dimensions," Physical Review E, Vol. 48, No. 5, 3998-4007, 1993.

23. Faddeev, L. D. and L. A. Takhtajan, Hamiltonian Methods in the Theory of Solitons, Springer Verlag, New York, 1987.

24. Fokas, A. S. and V. E. Zakharov, Important Developments in Soliton Theory, Springer Verlag, New York, 1993.

25. Forest, M. G., D. W. McLaughlin, D. J. Muraki, and O. C.Wright, "Nonfocusing instabilities in coupled, integrable nonlinear Schr¨odinger pdes," Journal of Nonlinear Science, Vol. 10, 291-331, 2000.

26. Gagnon, L. and P. A. Belanger, "Adiabatic amplification of optical solitons," Physical Review A, Vol. 43, No. 11, 6187-6193, 1991.

27. Ghidaglia, J. M. and J. C. Saut, "Nonexistence of travelling wave solutions to nonelliptic nonlinear Schr¨odinger equations," Journal of Nonlinear Science, Vol. 6, No. 2, 139-145, 1996.

28. Hasegawa, A. and Y. Kodama, Solitons in Optical Communications, Oxford University Press, UK, 1995.

29. Hayata, K. and M. Koshiba, "Solution of self-trapped multidimensional optical beams by Galerkin’s method," Optics Letters, Vol. 17, 841-843, 1992.

30. Hayata, K. and M. Koshiba, "Bright-dark solitary-wave solutions of a multi-dimensional nonlinear Schrodinger’s equation," Physical Review E, Vol. 48, No. 3, 2312-2315, 1993.

31. Hayata, K. and M. Koshiba, "Algebraic solitary-wave solutions of a nonlinear Schr¨odinger’s equation," Physical Review E, Vol. 51, No. 2, 1499-1502, 1995.

32. Infield, E. and G. Rowlands, Nonlinear Waves, Solitons and Chaos, Cambridge University Press, 1990.

33. Jovanoski, Z. and R. A. Sammut, "Propagation of Gaussian beams in a nonlinear saturable medium," Physical Review E, Vol. 50, No. 5, 4087-4093, 1994.

34. Karpman, V. I. and A. G. Shagalov, "Stability of solitons described the nonlinear Schrodinger-type equations with higher order dispersion," Physica D, Vol. 144, No. 1-2, 194-210, 2000.

35. Kivshar, Y. S. and B. A. Malomed, "Dynamics of solitons in nearly integrable systems," Reviews in Modern Physics, Vol. 61, No. 4, 765-915, 1989.

36. Kivshar, Y. S., "Bright and dark spatial solitons in non-Kerr media," Optical and Quantum Electronics, Vol. 30, 535-569, 1998.

37. Kivshar, Y. S. and B. Luther-Davis, "Dark optical solitons: physics and applications," Physics Reports, Vol. 298, 81-197, 1998.

38. Kivshar, Y. S. and D. E. Pelinovsky, "Self-focusing and transverse instabilities of solitary waves," Physics Reports, Vol. 331, 117-195, 2000.

39. Manassah, J. T., P. L. Baldeck, and R. R. Alfano, "Self-focusing, self-phase modulation, and diffraction in bulk homogenous material," Optics Letters, Vol. 13, 1090-1092, 1988.

40. Mcleod, R., K. Wagner, and S. Blair, "(3+1)-dimensional optical soliton dragging logic," Physical Review A, Vol. 52, No. 4, 3254-3278, 1995.

41. Mihalache, D., D. Mazilu, L. C. Crasovan, B. A. Malomed, and F. Lederer, "Three-dimensional spinning solitons in the cubicquintic nonlinear medium," Physical Review E, Vol. 61, No. 6, 7142-7145, 2000.

42. Mihalache, D., M. Bertolotti, and C. Cibilia, "Nonlinear wave propagation in planar structures," Progress in Optics, Vol. XXVII, 228-309, 1989.

43. Pelinovsky, D. E., V. V. Afanasjev, and Y. S. Kivshar, "Nonlinear theory of oscillating, decaying and collapsing solitons in the generalized nonlinear Schr¨odinger’s equation," Physical Review E, Vol. 53, No. 2, 1940-1953, 1996.

44. Silberberg, Y., "Collapse of optical pulses," Optics Letters, Vol. 15, 1282-1284, 1990.

45. Sonar, S., J. Kumar, and P. K. Sen, "Suppression of soliton instability by higher order nonlinearity in long haul optical communication systems," Journal of Nonlinear Optical Physics and Materials, Vol. 8, No. 4, 497-502, 1999.

46. Skarka, V., V. I. Berezhiani, and R. Miklaszewski, "Generation of light spatiotemporal solitons from asymmetric pulses in saturating nonlinear media," Physical Review E, Vol. 59, No. 1, 1270-1273, 1999.

47. Snyder, A. W. and D. J. Mitchell, "Spatial solitons of the powerlaw nonlinearity," Optics Letters, Vol. 18, No. 2, 101-103, 1993.

48. Sulem, C. and P. L. Sulem, The Nonlinear Schrodinger’s Equation, Springer Verlag, New York, 1999.

49. Yang, J. and D. J. Kaup, "Stability and evolution of solitary waves in perturbed generalized nonlinear Schrodinger’s equation," SIAM Journal of Applied Mathematics, Vol. 60, No. 3, 967-989, 2000.

50. Zhou, C., X. T. He, and T. Cai, "Pattern structures on generalized nonlinear Schrodinger’s equations with various nonlinear terms," Physical Review E, Vol. 50, No. 5, 4136-4155, 1994.