# American Institute of Mathematical Sciences

July  2019, 24(7): 3067-3075. doi: 10.3934/dcdsb.2018300

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

 1 School of Mathematical Sciences, Shanxi University, Taiyuan, 030006, China 2 School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

* Corresponding author: Xiong Li

Received  March 2018 Revised  July 2018 Published  October 2018

Fund Project: The second author is supported by NSF grant 11571041 and the Fundamental Research Funds for the Central Universities.

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.

Citation: Yang Wang, Xiong Li. Uniqueness of traveling front solutions for the Lotka-Volterra system in the weak competition case. Discrete & Continuous Dynamical Systems - B, 2019, 24 (7) : 3067-3075. doi: 10.3934/dcdsb.2018300
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