TITLE:
Lie Symmetries, One-Dimensional Optimal System and Optimal Reduction of (2 + 1)-Coupled nonlinear Schrödinger Equations
AUTHORS:
A. Li, Chaolu Temuer
KEYWORDS:
Nonlinear Schrödinger Equations, Lie Aymmetry Group, Lie algebra, Optimal System
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.2 No.7,
June
20,
2014
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.