Article Dans Une Revue Journal of Dynamics and Differential Equations Année : 2025

Asymptotic stability of fast solitary waves to the Benjamin Equation

Mohamad Darwich
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Luc Molinet

Résumé

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 $ γ<0$ which is the physical case.

Dates et versions

hal-05554628 , version 1 (16-03-2026)

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May Abdallah, Mohamad Darwich, Luc Molinet. Asymptotic stability of fast solitary waves to the Benjamin Equation. Journal of Dynamics and Differential Equations, 2025, 40 p. ⟨10.1007/s10884-025-10461-3⟩. ⟨hal-05554628⟩
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