Homoclinic manifolds, center manifolds and exact solutions of four-dimensional traveling wave systems for two classes of nonlinear wave equations

摘要

For the Lax KdV5 equation and the KdV-Sawada-Kotera-Ramani equation, their corresponding four-dimensional traveling wave systems are studied by using Congrove's method. Exact explicit gap soliton, embedded soliton, periodic and quasi-periodic wave solutions are obtained. The existence of homoclinic manifolds to three kinds of equilibria including a hyperbolic equilibrium, a center-saddle and an equilibrium with zero pair of eigenvalues is revealed. The bifurcation conditions of equilibria are given.