Asymptotic behavior and uniqueness of traveling wave solutions in Ricker competition system

The existence of traveling wave solutions connecting two half-positive equilibria in Ricker competition system can be obtained by the results (B. Li, H.F. Weinberger, M.A. Lewis, Spreading speeds as slowest wave speeds for cooperative systems, Math. Biosci. 196 (2005) 82–98). In this paper we first prove that any nondecreasing traveling wave solutions have the exponential decay asymptotic behavior at the minus/plus infinity by means of Ikeharaʼs Theorem, and then use the strong comparison principle and the sliding method to obtain the uniqueness of the traveling wave solutions for this system.