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Progress In Electromagnetics Research
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TEMPORAL 1-SOLITON SOLUTION OF THE COMPLEX GINZBURG-LANDAU EQUATION WITH POWER LAW NONLINEARITY

By A. Biswas

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Abstract:
This paper obtains the exact 1-soliton solution of the complex Ginzburg-Landau equation with power law nonlinearity that governs the propagation of solitons through nonlinear optical fibers. The technique that is used to carry out the integration ofthis eqyuation is He's semi-inverse variational principle.

Citation:
A. Biswas, " temporal 1 - soliton solution of the complex ginzburg - landau equation with power law nonlinearity ," Progress In Electromagnetics Research, Vol. 96, 1-7, 2009.
doi:10.2528/PIER09073108
http://www.jpier.org/PIER/pier.php?paper=09073108

References:
1. Biswas, A. and S. Konar, Introduction to Non-kerr Law Optical Solitons, CRC Press, Boca Raton, FL, USA, 2006.

2. Biswas, A., "Dynamics of Gaussian and super-Gaussian solitons in birefringent optical fibers," Progress In Electromagnetics Research, Vol. 33, 119-139, 2001.
doi:10.2528/PIER00101203

3. Biswas, A. and S. Konar, "Theory of dispersion-managed optical solitons," Progress In Electromagnetics Research, Vol. 50, 83-134, 2005.
doi:10.2528/PIER04051301

4. Biswas, A., "Stochastic perturbation of parabolic law optical solitons," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 11, 1479-1488, 2007.
doi:10.1163/156939307782000262

5. Biswas, A., D. Milovic, F. Majid, and R. Kohl, "Optical soliton sooling in a saturable law media," Journal of Electromagnetic Waves and Applications, Vol. 22, 1735-1746, 2008.
doi:10.1163/156939308786375163

6. Biswas, A., R. Kohl, M. E. Edwards, and E. Zerrad, "Soliton parameter dynamics in a non-Kerr law media," Progress In Electromagnetics Research C, Vol. 1, 1-35, 2008.
doi:10.2528/PIERC07121707

7. Khalique, C. M. and A. Biswas, "Optical solitons with parabolic and dual-power law nonlinearity via Lie symmetry analysis," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 7, 963-973, 2009.
doi:10.1163/156939309788355270

8. Kohl, R., A. Biswas, D. Milovic, and E. Zerrad, "Adiabatic dynamics of Gaussian and super-Gaussian solitons in Dispersion-Managed optical fibers," Progress In Electromagnetics Research, Vol. 84, 27-53, 2008.
doi:10.2528/PIER08052703

9. Kohl, R., A. Biswas, D. Milovic, and E. Zerrad, "Soliton perturbation theory for dispersion-managed optical fibers," Journal of Nonlinear Optical Physics and Materials, Vol. 18, No. 2, 227-270, 2009.
doi:10.1142/S0218863509004592

10. Kohl, R., A. Biswas, D. Milovic, and E. Zerrad, "Optical solitons by He's variational principle in a non-Kerr law media," Journal of Infrared, Millimeter and Terrahertz Waves, Vol. 30, No. 5, 526-537, 2009.
doi:10.1007/s10762-009-9467-9

11. Lott, D. A., A. Henriquez, B. J. M. Sturdevant, and A. Biswas, "A numerical study of optical soliton-like structures resulting from the nonlinear Schrodinger's equation with square-root law nonlinearity," Applied Mathematics and Computation, Vol. 207, No. 2, 319-326, 2009.
doi:10.1016/j.amc.2008.10.038

12. Mishra, M. and S. Konar, "Interaction of solitons in a dispersion-managed optical communication system with asymmetric dispersion map," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 4, 2049-2058, 2007.
doi:10.1163/156939307783152830

13. Mishra, M. and S. Konar, "High bit rate dense dispersion-managed optical communication systems with distributed amplification," Progress In Electromagnetics Research, Vol. 78, 301-320, 2008.
doi:10.2528/PIER07091305

14. Panajotovic, A., D. Milovic, and A. Biswas, "Influence of even order dispersion on soliton transmission quality with coherent interference," Progress In Electromagnetics Research B, Vol. 3, 63-72, 2008.
doi:10.2528/PIERB07120404

15. Shwetanshumala, S., S. Jana, and S. Konar, "Propagation of a mixture of modes of a laser beam in a medium with saturable nonlinearity," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 1, 65-77, 2006.
doi:10.1163/156939306775777422

16. Shwetanshumala, S. and A. Biswas, "Femtosecond pulse propagation in optical fibers under higher order effects: A collective variables approach," International Journal of Theoretical Physics, Vol. 47, No. 6, 1699-1708, 2008.
doi:10.1007/s10773-007-9611-z

17. Shwetanshumala, S., "Temporal solitons of modified complex Ginzburg-Landau equation," Progress In Electromagnetic Research Letters, Vol. 3, 17-24, 2008.
doi:10.2528/PIERL08010401

18. Srivastava, S., "Coupled bright-dark soliton pairs in polymeric photorefractive materials," Journal of Electromagnetic Waves and Applications, Vol. 22, No. 2--3, 335-342, 2008.
doi:10.1163/156939308784160730

19. Stojanovic, B., D. Milovic, and A. Biswas, "Timing shift of optical pulses due to inter-channel cross-talk," Progress In Electromagnetic Research M, Vol. 1, 21-30, 2008.
doi:10.2528/PIERM08012705

20. Sturdevant, B. J. M., D. A. Lott, and A. Biswas, "Dynamics of topological optical solitons with time-dependent dispersion, nonlinearity and attenuation," Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 8, 3305-3308, 2009.
doi:10.1016/j.cnsns.2008.12.014

21. Sturdevant, B., D. A. Lott, and A. Biswas, "Topological solitons in 1+2 dimensions with time-dependent coefficients," Progress In Electromagnetic Research Letters, Vol. 10, 69-75, 2009.

22. Sturdevant, B., D. A. Lott, and A. Biswas, Dark 1-soliton solution of the generalized Radhakrishnan, Kundu, Lakshmanan equation with nonlinear dispersion, Submitted.

23. Wazwaz, A. M., "Reliable analysis for nonlinear Schrodinger equations with a cubic nonlinearity and a power law nonlinearity ," Mathematical and Computer Modelling, Vol. 43, No. 1--2, 178-184, 2006.
doi:10.1016/j.mcm.2005.06.013

24. Wazwaz, A. M., "Exact solutions for the fourth order nonlinear Schrodinger equations with cubic and power law nonlinearities," Mathematical and Computer Modelling, Vol. 43, No. 7--8, 802-808, 2006.
doi:10.1016/j.mcm.2005.08.010

25. Wazwaz, A. M., "A study on linear and nonlinear Schrodinger equations by the variational iteration method," Chaos, Solitons and Fractals, Vol. 37, No. 4, 1136-1142, 2008.
doi:10.1016/j.chaos.2006.10.009


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