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

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

中国物理B ›› 2013, Vol. 22 ›› Issue (6): 60201-060201.doi: 10.1088/1674-1056/22/6/060201

• GENERAL • 下一篇

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

辛祥鹏, 陈勇, 王云虎

Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China

收稿日期:2012-10-16 修回日期:2012-12-15 出版日期:2013-05-01 发布日期:2013-05-01
基金资助:
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).

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

Xin Xiang-Peng (辛祥鹏), Chen Yong (陈勇), Wang Yun-Hu (王云虎)

Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China

Received:2012-10-16 Revised:2012-12-15 Online:2013-05-01 Published:2013-05-01
Contact: Chen Yong E-mail:ychen@sei.ecnu.edu.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: symmetry-preserving, potential systems, difference equation, Lie point symmetry

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.

Key words: symmetry-preserving, potential systems, difference equation, Lie point symmetry

中图分类号: (Group theory)

02.20.-a

04.60.Nc (Lattice and discrete methods)

辛祥鹏, 陈勇, 王云虎. A symmetry-preserving difference scheme for high dimensional nonlinear evolution equations[J]. 中国物理B, 2013, 22(6): 60201-060201.

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[J]. Chin. Phys. B, 2013, 22(6): 60201-060201.

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

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

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