Stability of Stochastically Forced Solitons in the Korteweg-de Vries Equation
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917997514326016 |
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| author | Westdorp, Rik W. S. Hupkes, Hermen Jan |
| author_facet | Westdorp, Rik W. S. Hupkes, Hermen Jan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17407 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability of Stochastically Forced Solitons in the Korteweg-de Vries Equation Westdorp, Rik W. S. Hupkes, Hermen Jan Analysis of PDEs Probability 60H15, 35Q53, 35C08 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. |
| title | Stability of Stochastically Forced Solitons in the Korteweg-de Vries Equation |
| topic | Analysis of PDEs Probability 60H15, 35Q53, 35C08 |
| url | https://arxiv.org/abs/2504.17407 |