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, Fabrice ; Gravejat, Philippe ; Smets, Didier
Annales de l'Institut Fourier, Tome 64 (2014), p. 19-70 / Harvested from Numdam
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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.

Publié le : 2014-01-01
DOI : https://doi.org/10.5802/aif.2838
Classification:  35B35,  35Q51,  35Q55
Mots clés: Équation de Gross-Pitaevskii, sommes de solitons, stabilité 
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     author = {B\'ethuel, Fabrice and Gravejat, Philippe and Smets, Didier},
     title = {Stability in the energy space for chains of~solitons of the one-dimensional Gross-Pitaevskii equation},
     journal = {Annales de l'Institut Fourier},
     volume = {64},
     year = {2014},
     pages = {19-70},
     doi = {10.5802/aif.2838},
     zbl = {06387265},
     mrnumber = {3330540},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2014__64_1_19_0}
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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) pp. 19-70. doi : 10.5802/aif.2838. http://gdmltest.u-ga.fr/item/AIF_2014__64_1_19_0/

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