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

Abstract

In this paper, we investigate the 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 Earth's rotation. We prove the existence of solitary waves by performing a phase plane analysis. Moreover, utilizing the approach proposed by Grillakis–Shatah–Strauss, we prove the stability of solitary waves.