Stability of Stochastically Forced Solitons in the Korteweg-de Vries Equation
Abstract
Abstract We study the stability and dynamics of solitons in the Korteweg-de Vries (KdV) equation in the presence of noise and deterministic forcing. The noise is space-dependent and statistically translation-invariant. We show that, for small forcing, solitons remain close to the family of traveling waves in a weighted Sobolev norm, with high probability. We study the effective dynamics of the soliton amplitude and position via their variational phase, for which we derive explicit modulation equations. The stability result holds on a time scale where the deterministic forcing induces significant amplitude modulation.
Fields of Study & Subjects
Advanced Mathematical Physics Problems
Nonlinear Waves and Solitons
Nonlinear Photonic Systems
Publication details
- Journal / source
- Stochastic Partial Differential Equations Analysis and Computations
- Publisher
- Springer Science and Business Media LLC
- Volume
- 14
- Issue
- 3
- Pages
- 1970–2023
- Publication date
- 20 February 2026
- Language
- EN