Burgers方程的非局域对称的局域化及对称约化
发布时间：2018-11-21 15:06
【摘要】：本文以对称方法为基本工具,围绕着对称的基本理论,研究了非线性偏微分方程,并给出了贝克隆变换及其新的群不变解。第一章简要介绍了对称的发展背景和研究现状,对本文相关的概念做了解释和说明,同时概括了本文的主要研究内容,并给出1+1维Burgers方程的李点对称及其群不变解。第二章利用了潘勒卫分析法中的WTC方法证明了Burgers方程是潘勒卫可积的。第三章根据截断潘勒卫展开法得到了Schwarz形式的Burgers方程并构造出Burgers方程的非局域对称,利用非局域对称局域化的思想求出自贝克隆变换及群不变解。最后我们将上面的方法进行了推广,根据截断潘勒卫展开法得到了Schwarz形式的Bu-rgers方程并构造出无穷多非局域对称,考虑到复杂性我们先研究n=2的非局域对称的情况,利用非局域对称局域化的思想求出自贝克隆变换及群不变解,特别还给出了孤子与Kummer波以及Airy波的新的相互作用解。
[Abstract]:In this paper, the nonlinear partial differential equations are studied by using the symmetric method as a basic tool, and around the basic theory of symmetry, and the Bayclon transformation and its new group invariant solutions are given. The first chapter briefly introduces the development background and research status of symmetry, explains and explains the related concepts in this paper, summarizes the main research contents of this paper, and gives the lie point symmetry and its group invariant solutions of 11-dimensional Burgers equation. In the second chapter, we prove that the Burgers equation is Pandler's integrable by using the WTC method in the Panlerweiss analysis method. In chapter 3, we obtain the Burgers equation in Schwarz form and construct the nonlocal symmetry of the Burgers equation according to the truncated Panlerweiser expansion method. We use the idea of nonlocal symmetry localization to obtain the solution derived from the Beacon transform and group invariant. Finally, we generalize the above method, obtain the Bu-rgers equation in Schwarz form and construct infinite nonlocal symmetries according to the truncated Panlerwey expansion method. Considering the complexity, we first study the case of nonlocal symmetry of NW 2. By using the idea of nonlocal symmetric localization, we obtain the solution derived from the Beacon transform and the group invariant solution. In particular, the new interaction solutions of soliton with Kummer wave and Airy wave are given.
【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
本文编号：2347328
[Abstract]:In this paper, the nonlinear partial differential equations are studied by using the symmetric method as a basic tool, and around the basic theory of symmetry, and the Bayclon transformation and its new group invariant solutions are given. The first chapter briefly introduces the development background and research status of symmetry, explains and explains the related concepts in this paper, summarizes the main research contents of this paper, and gives the lie point symmetry and its group invariant solutions of 11-dimensional Burgers equation. In the second chapter, we prove that the Burgers equation is Pandler's integrable by using the WTC method in the Panlerweiss analysis method. In chapter 3, we obtain the Burgers equation in Schwarz form and construct the nonlocal symmetry of the Burgers equation according to the truncated Panlerweiser expansion method. We use the idea of nonlocal symmetry localization to obtain the solution derived from the Beacon transform and group invariant. Finally, we generalize the above method, obtain the Bu-rgers equation in Schwarz form and construct infinite nonlocal symmetries according to the truncated Panlerwey expansion method. Considering the complexity, we first study the case of nonlocal symmetry of NW 2. By using the idea of nonlocal symmetric localization, we obtain the solution derived from the Beacon transform and the group invariant solution. In particular, the new interaction solutions of soliton with Kummer wave and Airy wave are given.
【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
【参考文献】
相关期刊论文 前1条
1 金艳;贾曼;楼森岳;;Nonlocalization of Nonlocal Symmetry and Symmetry Reductions of the Burgers Equation[J];Communications in Theoretical Physics;2012年12期
，本文编号：2347328
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