Abstract
For a class of (1 + 2)-dimensional nonlinear Schrodinger equations, the infinite dimensional Lie algebra of the classical symmetry group is found and the one-dimensional optimal system of an 8-dimensional subalgebra of the infinite Lie algebra is constructed. The reduced equations of the equations with respect to the optimal system are derived. Furthermore, the one-dimensional optimal systems of the Lie algebra admitted by the reduced equations are also constructed. Consequently, the classification of the twice optimal symmetry reductions of the equations with respect to the optimal systems is presented. The reductions show that the (1 + 2)-dimensional nonlinear Schrodinger equations can be reduced to a group of ordinary differential equations which is useful for solving the related problems of the equations.
Highlights
IntroductionWe plan to consider the (1 + 2)-dimensional coupled nonlinear Schrödinger (2D-CNLS) equations with cubic nonlinearity
We plan to consider the (1 + 2)-dimensional coupled nonlinear Schrödinger (2D-CNLS) equations with cubic nonlinearityHow to cite this paper: Li, A. and Temuer, C.L. (2014) Lie Symmetries, One-Dimensional Optimal System and Optimal Reduction of (2 + 1)-Coupled Nonlinear Schrödinger Equations
We show the optimal reduction classifications of the 2D-CNLS equations (1) through studying one-dimensional optimal system of the Lie algebra of the equations
Summary
We plan to consider the (1 + 2)-dimensional coupled nonlinear Schrödinger (2D-CNLS) equations with cubic nonlinearity. We show the optimal reduction classifications of the 2D-CNLS equations (1) through studying one-dimensional optimal system of the Lie algebra of the equations. Assuming that the 2D-CNLS equations (1) is invariant under the transformations (2), its real form transformed system is invariant under the Lie symmetry group with generator.
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