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

TL;DR

This paper investigates the existence, uniqueness, decay, and orbital stability of solitary wave solutions to the Benjamin equation, considering different speed regimes and the influence of a parameter in the equation.

Contribution

It establishes the conditions for existence, uniqueness, and stability of solitary waves for the Benjamin equation with a parameter, extending understanding of wave behavior across speed regimes.

Findings

Existence of solitary wave solutions for high and low speeds

Uniqueness and decay properties of these solutions

Orbital stability under certain conditions

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.