若干非线性PDEs守恒律的构造  

Construction of Conservation Laws for Some Nonlinear Partial Differential Equations

作　　者：赵巧红 张明霞 额尔敦布和[1,2] ZHAO Qiao-hong;ZHANG Ming-xia;Eerdunbuhe(College of Science,Inner Mongolia University of Technology,Hohhot 010051,China;School of Mathematics and Big Data,Hohhot Minzu College,Hohhot 010051,China)

机构地区：[1]内蒙古工业大学理学院,内蒙古呼和浩特010051 [2]呼和浩特民族学院数学与大数据学院,内蒙古呼和浩特010051

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2023年第1期87-94,共8页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11661034);全国高校黄大年式教师团队资助项目;内蒙古自治区“草原英才”工程产业创新人才团队资助项目。

摘　　要：利用对称-共轭对称‘对’方法和Ibragimov新守恒定理分别构造出Euler-Lagrange-type方程、CauchyKovalevskaya方程组及(2+1)维热方程中的诸多守恒律,同时通过对比已得守恒律发现两种守恒律方法的等价关系。结果对深入研究给定PDEs相关属性方面具有重要的理论意义。Conservation laws are important in the solution and reduction of the partial differential equations(PDEs) and have become hot research topic recently. Several conservation laws of Euler-Lagrangetype equation, Cauchy-Kovalevskaya equations and(2+1)-dimensional heat equation are constructed by using symmetry/adjoint symmetry pair method and Ibragimov’s new conservation theorem respectively.Meanwhile, the equivalence relation of conservation laws constructed by the two methods is confirmed through comparing them. The results are of important theoretical significance for further studying the related properties of the given PDEs.

关 键 词：偏微分方程 对称-共轭对称‘对’方法 Ibragimov新守恒定理 守恒律 

分 类 号：O175.29[理学—数学] O152.5[理学—基础数学]