Abstract: By using the bifurcation theory of dynamical systems to the coupled nonlinear wave equations, the existence and stability of periodic wave solutions by Hopf bifurcations are obtained. Theory of travelling wave was applied to transform a kind of coupled nonlinear wave equations into three-dimension dynamical systems. Under different parametric conditions, various sufficient conditions to guarantee the existence and stability of the above solutions are given.

Key words: travelling wave solution, Hopf bifurcation, nonlinear wave equation