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arXiv · 2307.15499

Long-Timescale Soliton Dynamics in the Korteweg-de Vries Equation with Multiplicative Translation-Invariant Noise

Rik W. S. Westdorp·Hermen Jan Hupkes
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Abstract

This paper studies the behavior of solitons in the Korteweg-de Vries equation under the influence of multiplicative noise. We introduce stochastic processes that track the amplitude and position of solitons based on a rescaled frame formulation and stability properties of the soliton family. We furthermore construct tractable approximations to the stochastic soliton amplitude and position which reveal their leading-order drift. We find that the statistical properties predicted by our method agree well with numerical evidence.

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Rik W. S. Westdorp, Hermen Jan Hupkes. 2023-07-28. Long-Timescale Soliton Dynamics in the Korteweg-de Vries Equation with Multiplicative Translation-Invariant Noise. https://doi.org/10.1016/j.physd.2024.134065

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