no. 19-20
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

Dias, João-Paulo1 ; Figueira, Mário1 ; Oliveira, Filipe2
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, Tome 348 (2010) no. 19-20, pp. 1079-1082.

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 :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.09.018
Dias, João-Paulo 1 ; Figueira, Mário 1 ; Oliveira, Filipe 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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Dias, João-Paulo; Figueira, Mário; Oliveira, Filipe. Existence of bound states for the coupled Schrödinger–KdV system with cubic nonlinearity. Comptes Rendus. Mathématique, Tome 348 (2010) no. 19-20, pp. 1079-1082. doi : 10.1016/j.crma.2010.09.018. http://www.numdam.org/articles/10.1016/j.crma.2010.09.018/

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