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

TL;DR

This paper investigates the properties and stability of solitary wave solutions to the rotation Benjamin-Ono equation, constructing a family of solutions, analyzing their convergence, and establishing their uniqueness under certain conditions.

Contribution

It introduces a new family of solitary wave solutions, proves their strong convergence, and establishes their uniqueness for small rotation parameters, improving previous stability results.

Findings

Constructed a family of even travelling wave solutions.

Proved strong convergence of the solution family.

Established uniqueness of solutions for small rotation parameters.

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.