Kundu方程与Novikov方程的某些精确解
发布时间：2018-07-20 14:57
【摘要】：非线性方程是描述自然界现象的一类重要的数学模型,也是数学物理特别是孤立子理论研究中的重要内容之一.本文利用非线性波的分支方法以及Mathematica软件等数学方法与工具,研究了两个非线性方程中的某些精确解.本文主要的研究工作如下:在第二章中,我们利用非线性波的分支方法研究Kundu方程某些行波解.通过一些特殊的轨道,我们获得了Kundu方程的一些新的显式行波解.我们的工作拓展了前人的结果.在第三章中,我们的主要目的是拓展关于带有三次非线性项的Novikov方程的一些结果.首先通过建立Novikov方程和另一个非线性方程的解之间的关系.然后基于非线性波的分支方法,我们给出了该非线性方程的某些精确行波解.最后,由这些行波解我们构造出Novikov方程的某些精确解.
[Abstract]:Nonlinear equation is an important mathematical model to describe natural phenomena, and it is also one of the important contents in the research of mathematical physics, especially soliton theory. In this paper some exact solutions of two nonlinear equations are studied by using the bifurcation method of nonlinear waves and mathematical methods and tools such as Mathematica software. The main work of this paper is as follows: in Chapter 2, we study some traveling wave solutions of Kundu equation by using the bifurcation method of nonlinear waves. Through some special orbits, we obtain some new explicit traveling wave solutions of Kundu equation. Our work extends the results of our predecessors. In chapter 3, our main purpose is to extend some results of Novikov equation with cubic nonlinear term. First, the relationship between the solutions of Novikov equation and another nonlinear equation is established. Then, based on the bifurcation method of nonlinear wave, we give some exact traveling wave solutions of the nonlinear equation. Finally, we construct some exact solutions of Novikov equation from these traveling wave solutions.
【学位授予单位】：华南理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175.29
本文编号：2133900
[Abstract]:Nonlinear equation is an important mathematical model to describe natural phenomena, and it is also one of the important contents in the research of mathematical physics, especially soliton theory. In this paper some exact solutions of two nonlinear equations are studied by using the bifurcation method of nonlinear waves and mathematical methods and tools such as Mathematica software. The main work of this paper is as follows: in Chapter 2, we study some traveling wave solutions of Kundu equation by using the bifurcation method of nonlinear waves. Through some special orbits, we obtain some new explicit traveling wave solutions of Kundu equation. Our work extends the results of our predecessors. In chapter 3, our main purpose is to extend some results of Novikov equation with cubic nonlinear term. First, the relationship between the solutions of Novikov equation and another nonlinear equation is established. Then, based on the bifurcation method of nonlinear wave, we give some exact traveling wave solutions of the nonlinear equation. Finally, we construct some exact solutions of Novikov equation from these traveling wave solutions.
【学位授予单位】：华南理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175.29
【参考文献】
相关博士学位论文 前1条
1 刘希强;非线性发展方程显式解的研究[D];中国工程物理研究院北京研究生部;2002年
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