For a class of (1 + 2)-dimensional nonlinear Schrodinger equations,
classical symmetry algebra is found and 1-dimensional optimal system, up to
conjugacy, is constructed. Its symmetry reductions are performed for each
class, and someexamples of exact invainvariant solutions are given.
References
[1]
Tajiri, M. (1983) Similarity Reductions of the One and Two Dimensional Nonlinear Schrodinger Equations. Journal of the Physical Society of Japan, 52, 1908-1917. http://dx.doi.org/10.1143/JPSJ.52.1908
[2]
Drazin, P.G. and Johnson, R.S. (1989) Solitons: An Introduction. Cambridge University Press, Cambridge. http://dx.doi.org/10.1017/CBO9781139172059
[3]
Kanth, A.S.V. and Aruna, K. (2009) Two-Dimensional Differential Transform Method for Solving Linear and NonLinear Schroedinger Equations. Chaos, Solitons & Fractals, 41, 2277-2281. http://dx.doi.org/10.1016/j.chaos.2008.08.037
[4]
Biswas, A. (2009) 1-Soliton Solution of 1+ 2 Dimensional Nonlinear Schrodinger’s Equation in Power Law Media. Communications in Nonlinear Science and Numerical Simulation, 14, 1830-1833. http://dx.doi.org/10.1016/j.cnsns.2008.08.003
[5]
Wazwaz, A.M. (2006) Reliable Analysis for Nonlinear Schrodinger Equations with a Cubic Nonlinearity and a Power Law Nonlinearity. Mathematical and Computer Modelling, 43, 178-184. http://dx.doi.org/10.1016/j.mcm.2005.06.013
[6]
Zhang, L.H. and Si, J.G. (2010) New Soliton and Periodic Solutions of (1 + 2)-Dimensional Nonlinear Schrodinger Equation with Dual-Power Law Nonlinearity. Communications in Nonlinear Science and Numerical Simulation, 15, 2747-2754. http://dx.doi.org/10.1016/j.cnsns.2009.10.028
[7]
Hydon, P.E. (2000) Symmetry Methods for Differential Equation. Cambridge University Press, Cambridge.
[8]
Bluman, G.W. and Kumei, S. (1991) Symmetries and Differential Equations. Springer-Verlag, Weinheim.
[9]
Chaolu, T. and Jing, P. (2010) An Algorithm for the Completes Symmetry Classification of Differential Equations Based on Wu’s Method. Journal of Engineering Mathematics, 66, 181-199. http://dx.doi.org/10.1007/s10665-009-9344-5