Traveling wave solutions of a competitive recursion

This paper is concerned with the traveling wave solutions of acompetitive recursion. By using a cross iteration scheme, we firstestablish the existence of traveling wave solutions, which are theinvasion waves of two competitive invaders. These wavesolutions are useful in understanding the long time behavior of solution of thecorresponding Cauchy type problem where the initial distribution is a perturbation of the wave profile of a traveling wave solution that may be nonmonotone.