Traveling wave solutions for Lotka-Volterra system re-visited

Abstract

Using a new method of monotone iteration of a pair of smooth lower- and upper-solutions, the traveling wave solutions of the classical Lotka-Volterra system are shown to exist for a family of wave speeds. Such con-structed upper and lower solution pair enables us to derive the explicit value f the minimal (critical) wave speed as well as the asymptotic decay/growth ates of the wave solutions at infinities. Furthermore, the traveling wave cor-responding to each wave speed is unique up to a translation of the origin. The tability of the traveling wave solutions with non-critical wave speed is also tudied by spectral analysis of a linearized operator in exponentially weighted anach spaces.