EXACT TRAVELLING WAVE SOLUTIONS AND THEIR DYNAMICAL BEHAVIOR FOR A CLASS COUPLED NONLINEAR WAVE EQUATIONS

For the system of KP like equation coupled to a Schriidinger equation, a corresponding four-dimensional travelling wave systems and a two-order linear non-autonomous system are studied by using Congrove's results and dynamical system method. For the four-dimensional travelling wave systems, exact explicit homoclinic orbit families, periodic and quasi-periodic wave solution families are obtained. The existence of homoclinic manifolds to four kinds of equilibria including a hyperbolic equilibrium, a center-saddle and an equilibrium with zero pair of eigenvalues is revealed. For the two-order linear non-autonomous system, the dynamical behavior of the bounded solutions is discussed.