The Existence Of Traveling Wave Solutions For Three Generalized KdV Equations

In this paper, by using the geometric singular perturbation theory, Melnikov method and monotone dynamical systems theory, we consider the existence of traveling wave solutions of three generalized KdV equations. As follows:Firstly introduces KdV equation, Burgers equation and traveling wave solutions, and main work of this paper.Secondly considers the existence of traveling wavefronts solutions of the modified Burgers-KdV equation with small long-range diffusion. Motivated by the analogue between traveling wavefronts and heteroclinic orbits of the corresponding ordinary differential equations, we apply the geometric singular perturbation theory to study the heteroclinic orbit, and prove the existence of traveling wave solution.Once again mainly discusses the existence of solitary wave solutions of a generalized KdV-KS equation. By employing the geometrical singular perturbation theory and Melnikov method to study the homoclinic orbit, we prove the existence of of solitary wave solutions.Final is concerned with the existence of traveling wavefronts solutions of the two-dimensional Burgers-KdV equation. We obtain a sufficient condition for two-dimensional Burgers-KdV equation by using monotone dynamical systems theory.