Traveling waves for a Lotka-Volterra competition system with diffusion

The paper addresses the existence of traveling waves for a two species competitive Lotka-Volterra reaction-diffusion system with discrete delays partial derivative/partial derivative t u(1)(chi, t) = d1 partial derivative(2)/partial derivative chi(2) u(1)(chi, t) + r(1)u(1)(chi, t)[1 - a(1)u(1)(chi, t) -b(1)u(1)(chi, t - tau(1)) - c(1)u(2)(chi, t - tau(2))], partial derivative/partial derivative t u(2)(chi, t) = d(2) partial derivative(2)/partial derivative chi 2 u(2)(chi, t) + r(2)u(2)(chi, t)[1 - a(2)u(2)(chi, t) -b(2)u(2)(chi, t - tau(3)) - c(2)u(1)(chi, t - tau 4)]. Our results can extend some existing ones for two species diffusion competition Lotka-Volterra systems. (C) 2010 Elsevier Ltd. All rights reserved.