Traveling waves for a system of equations

In this note, we improve the results given in [S. Ahmad, A.C. Lazer, An elementary approach to travelling front solutions to a system of NN competition–diffusion equations, Nonlinear Anal. 16 (10) (1991)] and [M.M. Tang, P.C. Fife, Propagating fronts for competing species equations with diffusion, Arch. Ration. Mech. Anal. 73 (1980)] by showing the existence of a traveling front solution for the system uit=diuixx+uifi(u1,…,un);1≤i≤n; (di>0di>0) under less restrictive assumptions.