非线性偏微分方程的非局域对称、相互作用解与守恒律

发布时间：2018-12-10 07:58

【摘要】：非线性偏微分方程是一门历史久远的学科,它是出现在各个科学领域中非常重要的数学模型.本文利用计算机代数为辅助工具,对非线性偏微分方程的三个问题进行了研究,它们分别是非局域对称、相互作用解以及守恒律.本文内容主要分为以下五部分:第一章,对非线性偏微分方程的解和守恒律的若干求法进行了简要的介绍,并阐明了本文的主要研究内容.第二章,详细阐述了论文所需要的基本理论知识.第三章,首先介绍了(2+1)-维Kaup-Kupershmidt方程组的背景知识,然后给出了关于该方程组的非局域对称和相互作用解.第四章,首先给出了Kadomtsev-Petviashvili势方程的相关研究背景,再运用Noether法得到了许多该方程的守恒律.第五章,对全文提出总结并作出展望.
[Abstract]:Nonlinear partial differential equation (NPDE) is a long history subject, and it is a very important mathematical model appearing in various fields of science. In this paper, three problems of nonlinear partial differential equations are studied by means of computer algebra. They are nonlocal symmetry, interaction solutions and conservation laws. The content of this paper is divided into the following five parts: the first chapter briefly introduces the solutions of nonlinear partial differential equations and some methods of finding conservation laws, and expounds the main research contents of this paper. The second chapter, elaborated the basic theory knowledge which the thesis needs. In chapter 3, the background knowledge of (21) -dimensional Kaup-Kupershmidt equations is introduced, and then the nonlocal symmetry and interaction solutions of the equations are given. In chapter 4, the research background of the Kadomtsev-Petviashvili potential equation is given, and then many conservation laws of the equation are obtained by using the Noether method. The fifth chapter, the full text proposed the summary and makes the prospect.
【学位授予单位】：宁波大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175.29

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