A symmetry-preserving difference scheme for high dimensional nonlinear evolution equations

doi:10.1088/1674-1056/22/6/060201

Abstract In this paper, a procedure for constructing discrete models of the high dimensional nonlinear evolution equations is presented. In order to construct the difference model, with the aid of the potential system of the original equation and compatibility condition, the difference equations which preserve all Lie point symmetries can be obtained. As an example, invariant difference models of the (2+1)-dimensional Burgers equation are presented.

Keywords: symmetry-preserving potential systems difference equation Lie point symmetry

Received: 16 October 2012
Revised: 15 December 2012
Accepted manuscript online:

PACS:	02.20.-a	(Group theory)
	04.60.Nc	(Lattice and discrete methods)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11075055 and 11275072), the Innovative Research Team Program of the National Natural Science Foundation of China (Grant No. 61021004), National High Technology Research and Development Program of China (Grant No. 2011AA010101), the Leading Academic Discipline Project of Shanghai (Grant No. B412), the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20120076110024), and the Shanghai Knowledge Service Platform Project (Grant No. ZF1213).

Corresponding Authors: Chen Yong
E-mail: ychen@sei.ecnu.edu.cn

Cite this article:

Xin Xiang-Peng (辛祥鹏), Chen Yong (陈勇), Wang Yun-Hu (王云虎) A symmetry-preserving difference scheme for high dimensional nonlinear evolution equations 2013 Chin. Phys. B 22 060201

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