一类非线形波动方程的分离变量解

发布时间：2018-05-31 07:28

本文选题：非线性波动方程 + 群分支法　；参考：《西北大学》2015年硕士论文

【摘要】：非线性现象广泛存在于数学、物理、生物等现代科学领域中,而这些现象大部分都可以抽象为某一种非线性方程,所以描述非线性问题的的演化方程越来越成为研究者们探讨的主要问题.比如在科学领域中把对于各种波浪现象(如水波,电磁波,光波,声波等)的描述转化为研究各种波动方程的相关性质,从而进一步解释相关现象.对于非线性问题的求解已经出现了很多方法,其中分离变量法是最为实用的方法之一,目前为止,已经有许多方法被用于研究非线性偏微分方程的分离变量解,包括几何法,Ansatz-based法,形式分离变量法等等.本文主要使用群分支法研究了一类非线性波动方程的泛函分离变量解,目标是寻找在每种情况下关于u的函数K(u),D(u),使得方程具有泛函分离变量解
[Abstract]:Nonlinear phenomena exist widely in modern science such as mathematics, physics, biology and so on, and most of these phenomena can be abstracted into some kind of nonlinear equation. Therefore, describing the evolution equations of nonlinear problems has become the main problem of researchers. For example, in the field of science, the description of various wave phenomena (such as water wave, electromagnetic wave, light wave, acoustic wave, etc.) is transformed into studying the related properties of various wave equations, so as to further explain the related phenomena. There have been many methods for solving nonlinear problems, among which the method of separating variables is one of the most practical methods. Up to now, many methods have been used to study the solutions of nonlinear partial differential equations. Including geometric method Ansatz-based method, formal separation of variables and so on. In this paper, the functional separation variable solutions of a class of nonlinear wave equations are studied by using group bifurcation method. The objective of this paper is to find the functional separation variable solutions of a class of nonlinear wave equations in each case.
【学位授予单位】：西北大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175.29

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