arXiv subjects

May Abdallah

Publications and source records attributed to May Abdallah.

2 recordsLinked to original sources

arXiv2024

Asymptotic stability of fast solitary waves to the Benjamin Equation

We prove the asymptotic stability of the high speed solitary waves to the Benjamin equation. This is done by establishing a Liouville property for the nonlinear evolution of the Benjamin equation around these solitary waves. To do this, inspired by Kenig-Martel-Robbiano 2011, we make use of the KdV limit of the Benjamin equation together with known rigidity property of the KdV flow. The main difficulties are linked to the presence of the Hilbert transform, that is a non-local operator, as well as the non-positivity of the quadratic part of the energy in the case $ \gamma<0$ which is the physical case.

math.AP↗

arXiv2024

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

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.

math.AP↗