Asymptotic nonlinear stability of traveling waves to a system of coupled Burgers equations

This paper is concerned with the existence and asymptotic nonlinear stability of traveling wave solutions to a system of coupled Burgers equations which arises in a number of various physical contexts. We establish the existence of traveling fronts based on the phase plane analysis method. The asymptotic nonlinear stability of traveling wave solutions is proved by the method of energy estimates. In contrast to the previous related results, our results do not require any smallness assumption on the wave strengths or on the coefficients.