Research On Existence Of Traveling Wave Solutions For Several Types Of Nonlinear Wave Equations

This dissertation deals with the existence of traveling wave solutions for a few nonlinear wave equations.We change nonlinear wave equations into traveling wave systems through variable substitution.Because traveling wavefronts(solitary wave solutions)are firmly connected with heteroclinic(homoclinic)orbits.We then prove that the traveling wave systems have heteroclinic(homoclinic)orbits,thus,the existence of traveling wavefronts(solitary wave solutions)for nonlinear wave equations are verified.This dissertation is divided into four parts.The main contents of the paper are as follows:In the first part,we mainly introduce the research background and main results.In the second part,we study the existence of traveling wavefronts for the Burgers-BBM equation.We find a suffcient condition for the existence on the basis of work of Weiguo Zhang and Mingliang Wang.In the third part,we study the existence of traveling wavefronts for the generalized Burgers-BBM equation when the perturbation parameter ? is suitably small.We prove the existence by using the geometric singular perturbation theory and the implicit theorem.In the four part,we study the existence of solitary wave solutions for the generalized KdV-KS equation.We prove that the solitary wave solutions persist when the perturbation parameter ? is suitably small by using the geometric singular perturbation theory.