Conservation laws of partial differential equations: Symmetry, adjoint symmetry and nonlinear self-adjointness

被引：7
|
作者：
Zhang, Zhi-Yong [1 ]
机构：
[1] North China Univ Technol, Coll Sci, Beijing 100144, Peoples R China
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2017年 / 74卷 / 12期
基金：
北京市自然科学基金; 中国国家自然科学基金;
关键词：
Nonlinear self-adjointness with differential substitution; Adjoint symmetry; Conservation law; Multiplier; DIRECT CONSTRUCTION METHOD; THEOREM;
D O I：
10.1016/j.camwa.2017.08.008
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Nonlinear self-adjointness method for constructing conservation laws of partial differential equations (PDEs) is further studied. We show that any adjoint symmetry of PDEs is a differential substitution of nonlinear self-adjointness and vice versa. Consequently, each symmetry of PDEs corresponds to a conservation law via a formula if the system of PDEs is nonlinearly self-adjoint with differential substitution. As a byproduct, we find that the set of differential substitutions includes the set of conservation law multipliers as a subset. The results are illustrated by three typical examples. (C) 2017 Published by Elsevier Ltd.
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页码：3129 / 3140
页数：12
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