On the Uniqueness and Orbital Stability of Slow and Fast Solitary Wave Solutions of the Benjamin Equation

Abstract

This paper is devoted to the study of existence and properties of solitary waves of the Benjamin equation. The studied equation includes a parameter $\gamma$ in front of the Benjamin-Ono term. We show the existence, uniqueness, decay and orbital stability of solitary wave solutions obtained as a solution to a certain minimization problem, associated either with high speeds without a sign condition on the parameter $\gamma$ or with low speeds for the appropriate sign.