no. 1
Stability in the energy space for chains of solitons of the one-dimensional Gross-Pitaevskii equation
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, Volume 64 (2014) no. 1, pp. 19-70.

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.

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.

DOI: 10.5802/aif.2838
Classification: 35B35, 35Q51, 35Q55
Keywords: Gross-Pitaevskii equation, sums of solitons, stability
Mots-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, Volume 64 (2014) no. 1, pp. 19-70. doi : 10.5802/aif.2838. https://aif.centre-mersenne.org/articles/10.5802/aif.2838/

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