Special Session 168: Stochastic Analysis and Large Scale Interacting Systems

Solitary Waves in a Stochastic Parametrically Forced Nonlinear Schr\odinger Equation
Manuel Gnann
TU Delft
Netherlands
Co-Author(s):    Rik Westdorp and Joris van Winden
Abstract:
We study a parametrically forced nonlinear Schr\odinger (PFNLS) equation, driven by multiplicative translation-invariant noise. We show that a solitary wave in the stochastic equation is orbitally stable on a timescale which is exponential in the inverse square of the noise strength. We give explicit expressions for the phase shift and fluctuations around the shifted wave which are accurate to second order in the noise strength. This is done by developing a new perspective on the phase-lag method introduced by Kr\uger and Stannat.