Synchronization by noise for traveling pulses

Abstract: We show synchronization by noise for stochastic partial differential equations which support traveling pulse solutions, such as the FitzHugh-Nagumo equation. We show that any two pulse-like solutions which start from different positions but are forced by the same realization of a multiplicative noise, converge to each other in probability on an appropriate time scale in the joint limit of small noise and long time. The noise is assumed to be Gaussian, white in time, colored and periodic in space, and non-degenerate only in the lowest Fourier mode. This is joint work with Christian Kuehn (TU Munich).