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

Xiang Peng Xin; Yong Chen; Yun Hu Wang

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

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

Xiang Peng Xin
, Yong Chen^*
, Yun Hu Wang

^*Corresponding author for this work

School of Mathematical Sciences

East China Normal University

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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.

Original language	English
Article number	060201
Journal	Chinese Physics B
Volume	22
Issue number	6
DOIs	https://doi.org/10.1088/1674-1056/22/6/060201
State	Published - Jun 2013

Keywords

Lie point symmetry
difference equation
potential systems
symmetry-preserving

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10.1088/1674-1056/22/6/060201

Cite this

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title = "A symmetry-preserving difference scheme for high dimensional nonlinear evolution equations",

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 = "Lie point symmetry, difference equation, potential systems, symmetry-preserving",

author = "Xin, \{Xiang Peng\} and Yong Chen and Wang, \{Yun Hu\}",

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AU - Xin, Xiang Peng

AU - Chen, Yong

AU - Wang, Yun Hu

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N2 - 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.

AB - 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.

KW - Lie point symmetry

KW - difference equation

KW - potential systems

KW - symmetry-preserving

UR - https://www.scopus.com/pages/publications/84880527291

U2 - 10.1088/1674-1056/22/6/060201

DO - 10.1088/1674-1056/22/6/060201

M3 - 文章

AN - SCOPUS:84880527291

SN - 1674-1056

VL - 22

JO - Chinese Physics B

JF - Chinese Physics B

IS - 6

M1 - 060201

ER -

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

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Keywords

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