On the existence and monotonicity of pulsating traveling waves for reaction–diffusion–advection systems in high dimensional and periodic media

Abstract

This paper is concerned with reaction–diffusion–advection systems posed in high dimensional and periodic media. Under certain conditions, we first prove that such systems admit pulsating traveling waves if and only if c≥c+∗(e), where c+∗(e) is the minimal wave speed. We also give a lower bound of the minimal wave speed. By establishing a comparison principle for pulsating traveling waves near the stable periodic steady solution, we further prove the monotonicity of pulsating traveling waves in the co-moving frame coordinate. These results generalize the known results for scalar equations and in the case when the system is invariant by translation along the direction of propagation. The obtained results are then applied to two species competition systems.