Existence of bound states for the coupled Schrödinger–KdV system with cubic nonlinearity

João-Paulo Dias; Mário Figueira; Filipe Oliveira

doi:10.1016/j.crma.2010.09.018

Partial Differential Equations

Existence of bound states for the coupled Schrödinger–KdV system with cubic nonlinearity
[Existence d'ondes solitaires pour le système couplé de Schrödinger–KdV avec non linearité cubique]

Présenté par : Gilles Lebeau

João-Paulo Dias ¹ ; Mário Figueira ¹ ; Filipe Oliveira ²

¹ CMAF/UL and FCUL, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal
² Dep. Matemática, FCT/UNL, Monte da Caparica, Portugal

Comptes Rendus. Mathématique, Volume 348 (2010) no. 19-20, pp. 1079-1082.

Résumé
Abstract

Nous prouvons dans cette Note l'existence d'une famille infinie d'ondes solitaires régulières pour le système couplé de Schrödinger–Korteweg–de Vries, qui décroissent exponentiellement a l'infini.

We prove in this Note the existence of an infinite family of smooth positive bound states for the coupled Schrödinger–Korteweg–de Vries system, which decays exponentially at infinity.

Reçu le : 2009-03-17
Accepté le : 2010-09-20
Publié le : 2010-10-01

DOI : 10.1016/j.crma.2010.09.018

Affiliations des auteurs :

João-Paulo Dias ¹ ; Mário Figueira ¹ ; Filipe Oliveira ²

¹ CMAF/UL and FCUL, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal
² Dep. Matemática, FCT/UNL, Monte da Caparica, Portugal

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     author = {Jo\~ao-Paulo Dias and M\'ario Figueira and Filipe Oliveira},
     title = {Existence of bound states for the coupled {Schr\"odinger{\textendash}KdV} system with cubic nonlinearity},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1079--1082},
     publisher = {Elsevier},
     volume = {348},
     number = {19-20},
     year = {2010},
     doi = {10.1016/j.crma.2010.09.018},
     language = {en},
}

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João-Paulo Dias; Mário Figueira; Filipe Oliveira. Existence of bound states for the coupled Schrödinger–KdV system with cubic nonlinearity. Comptes Rendus. Mathématique, Volume 348 (2010) no. 19-20, pp. 1079-1082. doi : 10.1016/j.crma.2010.09.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.09.018/

Bibliographie
Cité par

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