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Pré-Publication, Document De Travail Année : 2023

Linear asymptotic stability of small-amplitude periodic waves of the generalized Korteweg--de Vries equations

Résumé

In this note, we extend the detailed study of the linearized dynamics obtained for cnoidal waves of the Korteweg--de Vries equation in \cite{JFA-R} to small-amplitude periodic traveling waves of the generalized Korteweg-de Vries equations that are not subject to Benjamin--Feir instability. With the adapted notion of stability, this provides for such waves, global-in-time bounded stability in any Sobolev space, and asymptotic stability of dispersive type. When doing so, we actually prove that such results also hold for waves of arbitrary amplitude satisfying a form of spectral stability designated here as dispersive spectral stability.

Dates et versions

hal-04372277 , version 1 (04-01-2024)

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Corentin Audiard, L. Miguel Rodrigues, Changzhen Sun. Linear asymptotic stability of small-amplitude periodic waves of the generalized Korteweg--de Vries equations. 2023. ⟨hal-04372277⟩
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