This paper obtains the topological 1-soliton solution of the nonlinear Schrodinger's equation in 1+2 dimensions, with power law nonlinearity and time-dependent coefficients. The solitary wave ansatz is used to obtain the solution. It will also be proved that the power law nonlinearity must reduce to Kerr law nonlinearity for the topological solitons to exist.
2. Biswas, A., "Topological 1-soliton solution of the nonlinear Schrödinger's equation with Kerr law nonlinearity in 1+2 dimensions," Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 7, 2845-2847, 2009.
doi:10.1016/j.cnsns.2008.09.025
3. Escudero, C., "Blow-up of the hyperbolic Burger's equation," Journal of Statistical Physics, Vol. 127, No. 2, 327-338, 2007.
doi:10.1007/s10955-006-9276-7
4. Jordan, P. M., "Growth and decay of shock and accleration waves in a traffic flow model with relaxation," Physical D, Vol. 207, No. 3--4, 220-229, 2005.
doi:10.1016/j.physd.2005.06.002
5. 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
6. Konar, S., S. Jana, and S. Shwetanshumala, "Incoherently coupled screening photovoltaic spatial solitons in biased photovoltaic photorefractive crystals," Optics Communications, Vol. 273, No. 2, 324-333, 2007.
doi:10.1016/j.optcom.2007.01.051
7. Konar, S., S. Jana, and M. Mishra, "Induced focussing and all optical switching in cubic-quintic nonlinear media," Optics Communications, Vol. 255, No. 1--3, 114-129, 2005.
doi:10.1016/j.optcom.2005.05.038
8. Kudryashov, N. A. and N. B. Loguinova, "Be careful with expfunction method," Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 5, 1881-1890, 2009.
doi:10.1016/j.cnsns.2008.07.021
9. Kudryashov, N. A., "Seven common errors in finding exact solutions of nonlinear differential equations," Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 9--10, 3507-3529, 2009.
doi:10.1016/j.cnsns.2009.01.023
10. Lott, D. A., A. Henriquez, B. J. M. Sturdevant, and A. Biswas, "A numerical study of optical soliton-like structures resulting from the nonlinear Schrödinger'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
11. Makarenko, A. S., M. N. Moskalkov, and S. P. Levkov, "On blow-up solutions in turbulence," Physics Letters A, Vol. 235, No. 4, 391-397, 1997.
doi:10.1016/S0375-9601(97)00667-1
12. 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
13. Sulem, C. and P. Sulem, The Nonlinear SchrÄodinger's Equation, Springer Verlag, New York, NY, 1999.
14. Wazwaz, A. M., "Reliable analysis for nonlinear Schrödinger 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
15. Wazwaz, A. M., "A study on linear and nonlinear Schrödinger equations by the variational iteration method," Chaos, Solitons & Fractals, Vol. 37, No. 4, 1136-1142, 2008.
doi:10.1016/j.chaos.2006.10.009
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