SOLITARY WAVES IN A STOCHASTIC PARAMETRICALLY FORCED NONLINEAR SCHRÖDINGER EQUATION

作     者：Gnann, Manuel V. Westdorp, Rik W.S. van Winden, Joris 

作者机构：Delft Institute of Applied Mathematics Faculty of Electrical Engineering Mathematics and Computer Science Delft University of Technology Mekelweg 4 Delft2628 CD Netherlands Mathematical Institute Leiden University P.O. Box 9512 Leiden2300 RA Netherlands 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2024年

核心收录：

主　　题：Solitons 

摘      要：We study a parametrically forced nonlinear Schrödinger (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 Krüger and Stannat. Additionally, we show well-posedness of the equation in the fractional Bessel space Hs for any s ∈ [0, ∞), demonstrating persistence of *** Codes 37H30, 35C08, 35Q55, 35Q60, 35R60, 60H15 Copyright © 2024, The Authors. All rights reserved.