THE PROPAGATION OF TRAVELING WAVES FOR STOCHASTIC GENERALIZED KPP EQUATIONS

We study the existence and propagation of approximate travelling waves of generalized KPP equations with seasonal multiplicative white noise perturbations of Ito type. Three regimes of perturbation are considered: weak, mild, and strong. We show that weak perturbations have little effect on the wave-like solutions of the unperturbed equations, while strong perturbations essentially destroy the wave and force the solutions to die down. For mild perturbations, we show that there is a residual wave form but propagating at a different speed to that of the unperturbed equation. In the Appendix, J. G. Gaines illustrates these different regimes by computer simulations