On the stability of the solitary waves to the rotation Benjamin-Ono equation

Abstract

In this paper, we study several aspects of solitary wave solutions of the rotation Benjamin-Ono equation. By solving a minimization problem on the line, we construct a family of even travelling waves ${\psi }_{c,\gamma }$. We also study the strong convergence of this family and we establish the uniqueness of ${\psi }_{c,\gamma }$ for $\gamma$ small enough. Note that this improves the results in [5] where the stability of the set of ground states is proven.