Traveling Wave Solutions Of Two Kinds Of Integrable Systems

In this paper, we mainly discuss two kinds of integrable system of traveling wave solution. One of them is the reaction di?usion equation, the other is a nonlinear wave equation.In the second chapter, we mainly study the existence and uniqueness of traveling wave solutions of reaction di?usion equations. At the same time, we discuss the stability of traveling wave solutions of reaction di?usion equations. The reaction di?usion equation is integro di?erential equation for the coupling neural network. We only analysis a large wave front of travelling wave solution when Z > 0. According to the principle of derivation and the monotonicity of the knowledge, we obtain one and only one traveling wave solution of the wavefront of the travelling wave equation. In the following research, we establish a stability index function, we obtain the stability of traveling wave solutions of reaction di?usion equations on the complex plane.In the third chapter, we mainly focus on the research of a class of nonlinear wave equations. We are mainly looking for the exact traveling wave solutions of nonlinear wave equations. By using the bifurcation theory of dynamical systems, we obtain the solutions of the equations of phase diagram. We can get the exact solutions of the general form of equation. They are periodic solutions, kink wave solutions and solitary wave solutions. At the end of the article, we give an example of the m Kd V equation. We can find real forms of exact solutions of the example equation by our research methods of exact solutions.