本文選題：有界行波解 + 雙曲函數(shù)展開(kāi)法��； 參考：《貴州民族大學(xué)》2016年碩士論文

【摘要】：對(duì)非線(xiàn)性發(fā)展方程的研究是自然科學(xué)和工程技術(shù)中一個(gè)非常重要的課題,隨著近年來(lái)研究的不斷深入,許多作者已經(jīng)得到了一些非線(xiàn)性發(fā)展方程的研究成果。本文利用平面動(dòng)力系統(tǒng)理論、待定系數(shù)法、雙曲函數(shù)展開(kāi)法、指數(shù)函數(shù)展開(kāi)法等方法對(duì)非線(xiàn)性發(fā)展方程的有界行波解的精確表達(dá)式進(jìn)行研究,具體以下列方程為例:1.廣義Kd V-Burgers-Kuramoto方程:2.Zakharov-Rubenchik方程:首先對(duì)方程(Ⅰ)作行波變換,再進(jìn)行一次降冪運(yùn)算,得出其等價(jià)的平面動(dòng)力系統(tǒng),根據(jù)雅克比行列式的特征值特點(diǎn)對(duì)其進(jìn)行定性分析,利用齊次平衡法和雙曲函數(shù)展開(kāi)法給出了系統(tǒng)新的孤波解的精確表達(dá)式。對(duì)方程(II)先進(jìn)行行波變換,再將方程化成與之對(duì)應(yīng)的平面動(dòng)力系統(tǒng),利用平面動(dòng)力系統(tǒng)理論和方法對(duì)其進(jìn)行有限遠(yuǎn)處奇點(diǎn)分析,得出方程(II)存在一條同宿軌和一條異宿軌。根據(jù)等價(jià)平面動(dòng)力系統(tǒng)理論的同宿軌和異宿軌與方程(II)的鐘狀孤波解和扭狀孤波解之間的對(duì)應(yīng)關(guān)系,利用待定系數(shù)法和Maple軟件得到了方程(II)的鐘狀孤波解和扭狀孤波解的顯式表達(dá)式。
[Abstract]:The study of nonlinear evolution equations is a very important subject in natural science and engineering technology. With the development of research in recent years, many authors have obtained some research results of nonlinear evolution equations. In this paper, the exact expressions of the bounded traveling wave solutions of nonlinear evolution equations are studied by means of plane dynamic system theory, undetermined coefficient method, hyperbolic function expansion method and exponential function expansion method. The following equations are taken as an example: 1. Generalized Kd V-Burgers-Kuramoto equation: 2. Zakharov-Rubenchik equation: first of all, the equation (I) is transformed by traveling wave, and then the equivalent plane dynamic system is obtained. By using the homogeneous equilibrium method and the hyperbolic function expansion method, the exact expression of the new solitary wave solution of the system is given. The equation (II) is transformed by traveling wave first and then transformed into a plane dynamic system corresponding to it. The singular point of equation (II) is analyzed in finite distance by using the theory and method of plane dynamic system. It is concluded that there exists a homoclinic orbit and an heteroclinic orbit in equation (II). According to the correspondence between homoclinic orbit and heteroclinic orbit of equivalent plane dynamical system theory and bell solitary wave solution and torsional solitary wave solution of equation (II), The explicit expressions of bell solitary wave solution and torsional solitary wave solution of equation (II) are obtained by using undetermined coefficient method and Maple software.
【學(xué)位授予單位】：貴州民族大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類(lèi)號(hào)】：O175.29

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本文編號(hào)：2101219