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

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.