Multi-solitary waves for the one-dimensional Zakharov system

Guillaume Rialland

doi:10.5802/crmath.732

Article de recherche - Équations aux dérivées partielles

Multi-solitary waves for the one-dimensional Zakharov system
[Multi-solitons pour le système de Zakharov en une dimension]

Guillaume Rialland ¹

¹ Université de Paris-Saclay, UVSQ, CNRS, Laboratoire de Mathématiques de Versailles, 78000 Versailles, France

Comptes Rendus. Mathématique, Volume 363 (2025), pp. 283-321.

Résumé
Abstract

Étant données différentes vitesses $c_{1}, \dots, c_{K}$ , nous établissons dans ce papier l’existence d’une solution au système de Zakharov en dimension $1$ se comportant asymptotiquement comme un $K$ -soliton, chaque soliton voyageant à vitesse $c_{k}$ . La preuve est adaptée de précédents résultats pour les équations NLS et gKdV.

Given different speeds $c_{1}, \dots, c_{K}$ , in the present paper we establish the existence of a solution to the Zakharov system in dimension $1$ that behaves asymptotically like a $K$ -solitary wave, each wave travelling with speed $c_{k}$ . The proof is adapted from previous results for the NLS and gKdV equations.

Reçu le : 2025-01-13
Révisé le : 2025-02-07
Accepté le : 2025-02-08
Publié le : 2025-04-08

DOI : 10.5802/crmath.732

Classification : 37K40, 35Q51, 35Q55
Keywords: Zakharov system, multi-solitary waves, asymptotic behaviour
Mots-clés : Système de Zakharov, multi-solitons, comportement asymptotique

Affiliations des auteurs :

Guillaume Rialland ¹

¹ Université de Paris-Saclay, UVSQ, CNRS, Laboratoire de Mathématiques de Versailles, 78000 Versailles, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Multi-solitary waves for the one-dimensional {Zakharov} system},
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     language = {en},
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Guillaume Rialland. Multi-solitary waves for the one-dimensional Zakharov system. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 283-321. doi : 10.5802/crmath.732. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.732/

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