A Coupled Generalized Korteweg-de Vries System Driven by White Noise

Aissa Boukarou

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arXiv · 2510.23843

A Coupled Generalized Korteweg-de Vries System Driven by White Noise

Aissa Boukarou

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Abstract

In this paper, we investigate the Cauchy problem for the coupled generalized Korteweg-de Vries system driven by white noise. We prove local well-posedness for data in $ H^{s} \times H^{s},$ with $ s>1/2$. The key ingredients that we used in this paper are multilinear estimates in Bourgain spaces, the It\^o formula and a fixed point argument. Our result improves the local well-posedness result of Gomes and Pastor \cite{gomes2021solitary}.

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Aissa Boukarou. 2025-10-27. A Coupled Generalized Korteweg-de Vries System Driven by White Noise. https://arxiv.org/abs/2510.23843

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