Right and Wrong Ans\"atze for Nonlinear Waves in Stochastic PDEs

Abstract

I investigate the possibility that explicit solutions of stochastic reaction-diffusion equations can be found by multiplying the deterministic travelling waves with a stochastic exponent. This approach has become widespread in the literature in recent years. I will conclude that this approach is, in general, not a valid Ansatz and only works in the case of NLS-type equations in the Stratonovich interpretation.