Traveling waves for a system of equations (Q927959)

The authors establish the existence of a traveling front solution for the system of reaction-diffusion equations \[ {\partial u_i\over\partial t}= d_i{\partial^2 u_i\over\partial x^2}+ u_i f_i(u_1,\dots, u_n),\quad 1\leq i\leq n, \] \((d_i> 0)\) under less restrictive assumptions as in a previous paper by the first two authors [Nonlinear Anal., Theory Methods Appl. 16, No.~10, 893--901 (1991; Zbl 0737.35029)]. Especially, they assume that \(f\) is only locally Lipschitzian.