Uniqueness of traveling front solutions for the Lotka-Volterra system in the weak competition case

Abstract

In this paper, we will prove the uniqueness of traveling front solutions with critical and noncritical speeds, connecting the origin and the positive equilibrium, for the classical competitive Lotka-Volterra system with diffusion in the weak competition, which partially answers the open problem presented by Tang and Fife in [17]. In fact, once these traveling front solutions have the same wave speed and the same asymptotic behavior at ξ = ±∞, they are unique up to translation.