三类非线性偏微分方程(组)的守恒律  

Conservation Laws for Third Types of Nonlinear Partial Differential Equations

作　　者：刘欣 额尔敦布和[1,2] 刘亚峰 温颖 LIU Xin;Eerdunbuhe;LIU Yafeng;WEN Ying(College of Science,Inner Mongolia University of Technology,Hohhot 010051,China;School of Mathematical Sciences,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科学学院,内蒙古呼和浩特010051

出　　处：《内蒙古民族大学学报（自然科学版）》2024年第5期74-80,共7页Journal of Inner Mongolia Minzu University：Natural Sciences Edition

基　　金：内蒙古自治区直属高校基本科研业务费项目(ZSLJ202203)。

摘　　要：非线性偏微分方程在多个学科领域中扮演着关键角色,其守恒律的求解是研究的核心之一。基于Lie对称性,并结合Maple等数学软件,应用对称-共轭对称‘对’方法和Ibragimov新守恒定理,推导不同方程的守恒律。通过比较这2种方法在同一方程上的应用结果,总结了各自的优势和适用性,从而为实际问题选择合适的求解策略提供了有价值的结论。Nonlinear partial differential equations play a crucial role in various disciplines,with solving their conservation laws being a core research focus.Utilizing Lie symmetry and leveraging mathematical software such as Maple,the author has applied both the symmetry/adjoint symmetry pair method and Ibragimov’s new conservation theorem to present the conservation laws of different equations.By comparing the application results of these two methods on the same equation,the advantages and applicability of each method are summarized,and valuable conclusions are provided for selecting suitable solution strategies for practical problems.

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

分 类 号：O175.29[理学—数学]