Traveling wave solutions for Lotka-Volterra system re-visited
Anthony W. Leung - Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45219, United States (email)
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 constructed upper and lower solution pair enables us to derive the explicit value of the minimal (critical) wave speed as well as the asymptotic decay/growth rates of the wave solutions at infinities. Furthermore, the traveling wave corresponding to each wave speed is unique up to a translation of the origin. The stability of the traveling wave solutions with non-critical wave speed is also studied by spectral analysis of a linearized operator in exponentially weighted Banach spaces.
Keywords: Traveling Wave, Existence, Monotone Iteration,
Asymptotic rates, Uniqueness, Spectrum, Stability.
Received: December 2009; Revised: September 2010; Available Online: October 2010.
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