| Recently;the study on dynamic behavior of traveling wave solutions of nonlinear mathematical physics equations is one of hot issues that many mathematics, mechanics, life sciences, geoscience, theoretical physics and engineering science workers focus on. It plays an irreplaceable role on nonlinear science. We have many effective methods for solving nonlinear mathematical physics equations so far, but given the substantive difficulties of solving exactly, we have not yet found an universal method of solving equa-tion, so looking for other feasible accurate solution and analysing dynamic behavior of traveling wave solutions is still a very challenging task.Based on the above-mentioned purposes, this paper summarizes and induces some frequently-used accurate solutions of nonlinear mathematical physics equations, explores a class of nonlinear mathematical physics equations which have practical application background, such as Klein-Gordon cquation, Chaffee-Infante reaction-diffusion equation, Kolmogorov-Petrovskii-Piskunov equation, Zhiber-Shabat equation, Fitzhugh-Nagumo equation, Sharma-Tasso-Olever equation and Fisher equation, applys method of qual-itative theory of ordinary differential equation to analyse their traveling wave systems, finds the sufficient conditions for the existence of periodic wave solutions and solitary wave solutions for some equations by solving the closed orbits, homoclinic orbits and heteroclinic orbits of planar systems, and gives their expressions. Given the computational complexity, the kink solitary wave solutions currently found are mostly determined by the parabolic solutions of ordinary differential equations. This paper notices that Klein-Gordon equation, Zhiber-Shabat equation and Sharma-Tasso-Olever equation have the kink solitary wave solutions determined by the nonparabolic solutions of ordinary differential equations. Similarly in the existing literatures, the periodic wave solutions currently found are mostly determined by the closed orbits of ordinary differential equations. This paper notices the periodic wave solutions of Chaffee-Infante reaction-diffusion equation and Fisher equation determined by the limit cycles of their traveling wave sys-tems by bifurcation theory.This paper is divided into9chapters altogether. The first chapter primarily introduces and summa-rizes the study on dynamic behavior of traveling wave solutions of nonlinear mathematical physics equa-tions, and gives the main conclusions of this paper. The second chapter introduces some knowledge about solitary wave solutions and periodic wave solutions for nonlinear mathematical physics equations and lays the foundation for the main work of this paper. The third chapter discusses the periodic wave solutions and solitary wave solutions for Klein-Gordon equation. The fourth chapter discusses the kink solitary wave solutions, anti-kink wave solutions and periodic wave solutions for Chaffee-Infante reaction-diffusion equation. The fifth chapter discusses the kink solitary wave solutions and anti-kink wave solutions for Kolmogorov-Petrovskii-Piskunov equation. The sixth chapter discusses the kink solitary wave solutions and anti-kink wave solutions for Zhiber-Shabat equation. The seventh chapter discusses the kink solitary wave solutions and anti-kink wave solutions for Fitzhugh-Nagumo equation. The eighth chapter discusses the kink solitary wave solutions and anti-kink wave solutions for Sharma-Tasso-Olever equation. The ninth chapter discusses the periodic wave solutions for Fisher equation. All conclusions of this paper are drawn from the9chapters above. |
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