Right and Wrong Ans\"atze for Nonlinear Waves in Stochastic PDEs
Analysis of PDEs
2026-03-27 v2
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.
Cite
@article{arxiv.2508.12786,
title = {Right and Wrong Ans\"atze for Nonlinear Waves in Stochastic PDEs},
author = {C. H. S. Hamster},
journal= {arXiv preprint arXiv:2508.12786},
year = {2026}
}