Persistence of travelling waves for a coupled nonlinear wave system

In this paper, we study a sort of coupled nonlinear wave system. Special attention is paid to the question of the existence of heteroclinic orbits of the associated ordinary differential equation from the geometric singular perturbation point of view. We prove that a solitary wave persists when the perturbation parameter is suitably small. This argument does not require an explicit expression for the original coupled nonlinear wave system.