The Study Of The Traveling Wave Solutions Of Three Kinds Of Nonlinear Wave Equations

The paper study the persistence of the traveling fronts of the Musca domestica equation with long-range diffusion, the persistence of the solitary wave solutions of the singularly perturbed ZK-KS equation, the existence of the traveling fronts of the RLW-Burgers equation by using geometric singular perturbation theory, the method of the Melnikov function and monotone dynamical systems theory.The paper introduce the research background of the traveling wave solutions of the nonlinear wave equations, the related research work of some scholars and the main research work and results of this paper.And the paper study the persistence of traveling fronts of the Musca domestica equation with long-range diffusion. Motivated by the analogy between traveling fronts and heteroclinic orbits of the corresponding ordinary differential equation, we prove the persistence of these waves for sufficiently small dissipation from the geometric singular perturbation point of view. Namely, the population quantity will finally reach a steady state, if it is nonzero at begin.Then we study the solitary wave solutions of the singularly perturbed ZK-KS equation by using the geometric singular perturbation theory and the method of Melnikov function, and prove the persistence of these waves for sufficiently small perturbation.In the last we study the traveling fronts of the RLW-Burgers equation by using monotone dynamical systems theory and prove the existence of these waves for sufficiently small perturbation, and obtain a sufficient condition of the existence. Furthermore, the existent condition of the discovered partial exact solutions is one of our condition.