On the stability of the solitary waves to the (generalized) kawahara equation - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2016

On the stability of the solitary waves to the (generalized) kawahara equation

Résumé

In this paper we investigate the orbital stability of solitary waves to the (generalized) Kawahara equation (gKW) which is a fifth order dispersive equation. For some values of the power of the nonlinearity, we prove the orbital stability in the energy space H 2 (R) of two branches of even solitary waves of gKW by combining the well-known spectral method introduced by Benjamin [3] with continuity arguments. We construct the first family of even solitons by applying the implicit function theorem in the neighborhood of the explicit solitons of gKW found by Dey et al. [8]. The second family consists of even travelling waves with low speeds. They are solutions of a constraint minimization problem on the line and rescaling of perturbations of the soliton of gKdV with speed 1.
Fichier principal
Vignette du fichier
Stability-gKW.pdf (298.84 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01403360 , version 1 (25-11-2016)

Identifiants

Citer

André Kabakouala, Luc Molinet. On the stability of the solitary waves to the (generalized) kawahara equation. 2016. ⟨hal-01403360⟩
152 Consultations
225 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More