Vol. 36
Latest Volume
All Volumes
PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
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
http://www.jpier.org/PIER/pier.php?paper=0111052
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.