【摘要】：非線性方程是描述自然界現(xiàn)象的一類重要的數(shù)學(xué)模型,也是數(shù)學(xué)物理特別是孤立子理論研究中的重要內(nèi)容之一.本文利用非線性波的分支方法以及Mathematica軟件等數(shù)學(xué)方法與工具,研究了兩個(gè)非線性方程中的某些精確解.本文主要的研究工作如下:在第二章中,我們利用非線性波的分支方法研究Kundu方程某些行波解.通過(guò)一些特殊的軌道,我們獲得了Kundu方程的一些新的顯式行波解.我們的工作拓展了前人的結(jié)果.在第三章中,我們的主要目的是拓展關(guān)于帶有三次非線性項(xiàng)的Novikov方程的一些結(jié)果.首先通過(guò)建立Novikov方程和另一個(gè)非線性方程的解之間的關(guān)系.然后基于非線性波的分支方法,我們給出了該非線性方程的某些精確行波解.最后,由這些行波解我們構(gòu)造出Novikov方程的某些精確解.
[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.
【學(xué)位授予單位】：華南理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：O175.29

【參考文獻(xiàn)】

相關(guān)博士學(xué)位論文 前1條

1 劉希強(qiáng);非線性發(fā)展方程顯式解的研究[D];中國(guó)工程物理研究院北京研究生部;2002年

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本文編號(hào)：2133900