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Temuer, C. and Bai, Y.S. (2010) A New Algorithmic Theory for Determining and Classifying Classical and NonClassical Symmetries of Partial Differential Equations (in Chinese). Scientia Sinica Mathematica, 40, 331-348.

has been cited by the following article:

• 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.