[Solitons périodiques du système de Davey–Stewartson elliptique–elliptique focalisant]
Nous considérons les équations de Davey–Stewartson focalisantes dans le cas elliptique–elliptique, lorsqu'elles possèdent une solution unidimensionnelle de type soliton. En utilisant des méthodes de la théorie des systèmes dynamiques, nous montrons l'existence d'une famille de solutions bidimensionnelles qui ont le profil d'un soliton dans la direction spatiale longitudinale et sont périodiques dans la direction spatiale transverse. Nous montrons également que le soliton unidimensionnel est linéairement instable vis-à-vis des perturbations transverses.
We consider the elliptic–elliptic, focussing Davey–Stewartson equations, which have an explicit bright line soliton solution. The existence of a family of periodic solitons, which have the profile of the line soliton in the longitudinal spatial direction and are periodic in the transverse spatial direction, is established using dynamical systems arguments. We also show that the line soliton is linearly unstable with respect to perturbations in the transverse direction.
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@article{CRMATH_2016__354_5_486_0,
author = {Groves, Mark D. and Sun, Shu-Ming and Wahl\'en, Erik},
title = {Periodic solitons for the elliptic{\textendash}elliptic focussing {Davey{\textendash}Stewartson} equations},
journal = {Comptes Rendus. Math\'ematique},
pages = {486--492},
publisher = {Elsevier},
volume = {354},
number = {5},
year = {2016},
doi = {10.1016/j.crma.2016.02.005},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/j.crma.2016.02.005/}
}
TY - JOUR AU - Groves, Mark D. AU - Sun, Shu-Ming AU - Wahlén, Erik TI - Periodic solitons for the elliptic–elliptic focussing Davey–Stewartson equations JO - Comptes Rendus. Mathématique PY - 2016 SP - 486 EP - 492 VL - 354 IS - 5 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2016.02.005/ DO - 10.1016/j.crma.2016.02.005 LA - en ID - CRMATH_2016__354_5_486_0 ER -
%0 Journal Article %A Groves, Mark D. %A Sun, Shu-Ming %A Wahlén, Erik %T Periodic solitons for the elliptic–elliptic focussing Davey–Stewartson equations %J Comptes Rendus. Mathématique %D 2016 %P 486-492 %V 354 %N 5 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2016.02.005/ %R 10.1016/j.crma.2016.02.005 %G en %F CRMATH_2016__354_5_486_0
Groves, Mark D.; Sun, Shu-Ming; Wahlén, Erik. Periodic solitons for the elliptic–elliptic focussing Davey–Stewartson equations. Comptes Rendus. Mathématique, Tome 354 (2016) no. 5, pp. 486-492. doi : 10.1016/j.crma.2016.02.005. http://archive.numdam.org/articles/10.1016/j.crma.2016.02.005/
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