Answers are grounded in this paper and cite their sources.
Analysis shows that stability of solitons is maintained despite noise in the Korteweg-de Vries equation, indicating resilience under deterministic forcing.
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.
No takes yet. Share an insight, caveat, or question.
Westdorp et al. (2025) studied this question.
Synapse has enriched 8 closely related papers on similar clinical questions. Consider them for comparative context: