Lie symmetry analysis, Lie-Bäcklund symmetries, explicit solutions, and conservation laws of Drinfeld-Sokolov-Wilson system

Boundary value problems

Yufeng Zhang¹  Zhonglong Zhao² 

[1] College of Mathematics, China University of Mining and Technology, Xuzhou, P.R. China;Department of Mathematics, Harbin Institute of Technology, Harbin, P.R. China

关键词: Drinfeld-Sokolov-Wilson system;    optimal system;    Lie-Bäcklund symmetries;    explicit solutions;    conservation laws;    76M60;    34A05;    70S10;   

DOI  :  10.1186/s13661-017-0885-7

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The symmetry analysis method is used to study the Drinfeld-Sokolov-Wilson system. The Lie point symmetries of this system are obtained. An optimal system of one-dimensional subalgebras is derived by using Ibragimov’s method. Based on the optimal system, similarity reductions and explicit solutions of the system are presented. The Lie-Bäcklund symmetry generators are also investigated. Furthermore, the method of constructing conservation laws of nonlinear partial differential equations with the aid of a new conservation theorem associated with Lie-Bäcklund symmetries is presented. Conservation laws of the Drinfeld-Sokolov-Wilson system are constructed by using this method.

【 授权许可】

CC BY