Stochastic generalised KPP equations

Abstract

We classify multiplicative white noise perturbationsk(·)dw, of generalised KPP equations and their effects on deterministic approximate travelling wave solutions by the behaviour of, the solutions of the stochastic generalised KPP equations converge to deterministic approximate travelling waves and ifbeing an associated potential energy, Фsa solution of the corresponding classical mechanical equations of Newton,Dbeing a certain domain inR1×Rrthen the white noise perturbations essentially destroy the wave structure and force the solutions to die down.For the case(suppose the existence of the limit) we show that there is a residual wave form but propagating at a different speed from that of the unperturbed equations. Numerical solutions are included and give good agreement with theoretical results.