Modulation analysis of the stochastic Camassa-Holm equation with pure jump noise

Yong Chen; Jinqiao Duan; Hongjun Gao; Xingyu Guo

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arXiv · 2303.04981

Modulation analysis of the stochastic Camassa-Holm equation with pure jump noise

Yong Chen·Jinqiao Duan·Hongjun Gao·Xingyu Guo

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Abstract

We study the stochastic Camassa-Holm equation with pure jump noise. We prove that if the initial condition of the solution is a solitary wave solution of the unperturbed equation, the solution decomposes into the sum of a randomly modulated solitary wave and a small remainder. Moreover, we derive the equations for the modulation parameters and show that the remainder converges to the solution of a stochastic linear equation as amplitude of the jump noise tends to zero.

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BibTeX RIS

Yong Chen, Jinqiao Duan, Hongjun Gao, Xingyu Guo. 2023-03-09. Modulation analysis of the stochastic Camassa-Holm equation with pure jump noise. https://arxiv.org/abs/2303.04981

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