Stability in the energy space for chains of solitons of the one-dimensional Gross-Pitaevskii equation
[Stabilité dans l’espace d’énergie pour les chaînes de solitons de l’équation de Gross-Pitaevskii en dimension un]
Béthuel, Fabrice1 ; Gravejat, Philippe2 ; Smets, Didier1
1 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Boîte Courrier 187, 75252 Paris Cedex 05, France.
2 Centre de Mathématiques Laurent Schwartz, École Polytechnique, 91128 Palaiseau Cedex, France.
Annales de l'Institut Fourier, Tome 64 (2014) no. 1, pp. 19-70.

Nous démontrons en dimension un la stabilité dans l’espace d’énergie des sommes de solitons de l’équation de Gross-Pitaevskii, dont les vitesses sont non nulles et deux-à-deux distinctes, et dont les positions initiales sont suffisamment espacées et ordonnées selon les vitesses des solitons.

We establish the stability in the energy space for sums of solitons of the one-dimensional Gross-Pitaevskii equation when their speeds are mutually distinct and distinct from zero, and when the solitons are initially well-separated and spatially ordered according to their speeds.

DOI : 10.5802/aif.2838
Classification : 35B35, 35Q51, 35Q55
Keywords: Gross-Pitaevskii equation, sums of solitons, stability
Mot clés : Équation de Gross-Pitaevskii, sommes de solitons, stabilité
Béthuel, Fabrice 1 ; Gravejat, Philippe 2 ; Smets, Didier 1

1 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Boîte Courrier 187, 75252 Paris Cedex 05, France.
2 Centre de Mathématiques Laurent Schwartz, École Polytechnique, 91128 Palaiseau Cedex, France. 
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Béthuel, Fabrice; Gravejat, Philippe; Smets, Didier. Stability in the energy space for chains of solitons of the one-dimensional Gross-Pitaevskii equation. Annales de l'Institut Fourier, Tome 64 (2014) no. 1, pp. 19-70. doi : 10.5802/aif.2838. http://www.numdam.org/articles/10.5802/aif.2838/

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