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arXiv · 2305.00631

Existence and stability of solitary waves to the rotation-Camassa-Holm equation

Hao Tong·Shaojie Yang
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Abstract

In this paper, we investigate existence and stability of solitary waves to the rotation-Camassa-Holm equation which can be considered as a model in the shallow water for the long-crested waves propagating near the equator with effect of the Coriolis force due to the Earths rotation. We prove existence of solitary waves by performing a phase plane analysis. Moreover, utilizing the approach proposed by Grillakis-Shatah-Strauss, we prove stability of solitary waves.

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Hao Tong, Shaojie Yang. 2023-05-01. Existence and stability of solitary waves to the rotation-Camassa-Holm equation. https://arxiv.org/abs/2305.00631

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