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Research on the Bifurcations of Traveling Wave Solutions for Several Classes of Nonlinear Wave Equations

Author: ZhangKeLei
Tutor: TangShengQiang
School: Guilin University of Electronic Science and Technology
Course: Basic mathematics
Keywords: Nonlinear wave equation Phase diagram Traveling wave solutions for branch Traveling wave solutions Three-step method
CLC: O175.29
Type: Master's thesis
Year: 2010
Downloads: 82
Quote: 0
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Abstract


This article from the perspective of dynamical systems theory to study the branch several nonlinear wave equation traveling wave solutions for the branch , and take advantage of integrable wave systems integrator and phase diagram of the first to study the nonlinear wave equation explicit and exact traveling wave solutions , and difficult to obtain in the case of explicit exact solutions , using the qualitative theory of differential equations for smooth and non- smooth traveling wave solutions to analyze the existence of text is divided into six chapters. the first chapter is the introduction , brief description of nonlinear wave equations development history , current status and significance of the second chapter is the preliminaries , introduces Professor Li Jibin proposed research odd nonlinear wave equations dynamical systems approach - \Law \system into a regular system , the use of singular systems and canonical distinctions and contacts gained in the different parameters of various smooth traveling wave solutions and non- smooth periodic wave solutions exist sufficient condition to explain nonsmooth periodic sharp wave generator causes. fourth chapter , the application of \smooth and non- smooth periodic wave solutions and in different regions of the parameter space is given solitary wave solutions, kink wave solutions and antikink wave solutions , tight solution, infinitely many smooth and non- smooth periodic wave solutions exist sufficient conditions , and calculated the precise parameters of some of the above expressions fifth chapter , the application of dynamical systems theory to study the long-wave approximation of shallow water equations exact traveling wave solutions in different regions of the parameter space is given Peakons , kink waves and anti- kink wave solutions and periodic wave solutions of infinite smooth sufficient conditions for existence , and calculate the number of explicit and exact traveling wave solutions of Chapter VI is a summary and outlook on this article summarizes the work proposed need to be further addressed.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Partial Differential Equations > Nonlinear partial differential equations
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