Two soliton collision for nonlinear Schrödinger equations in dimension 1

Perelman, Galina

Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011), p. 357-384 / Harvested from Numdam

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Résumé

We study the collision of two solitons for the nonlinear Schrödinger equation $i ψ_{t} = - ψ_{x x} + F ({| ψ |}^{2}) ψ$ , $F (ξ) = - 2 ξ + O (ξ^{2})$ as $ξ \to 0$ , in the case where one soliton is small with respect to the other. We show that in general, the two soliton structure is not preserved after the collision: while the large soliton survives, the small one splits into two outgoing waves that for sufficiently long times can be controlled by the cubic NLS: $i ψ_{t} = - ψ_{x x} - 2 {| ψ |}^{2} ψ$ .

Publié le : 2011-01-01

MR 2795711 | Zbl 1217.35176

DOI : https://doi.org/10.1016/j.anihpc.2011.02.002

@article{AIHPC_2011__28_3_357_0,
     author = {Perelman, Galina},
     title = {Two soliton collision for nonlinear Schr\"odinger equations in dimension 1},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {28},
     year = {2011},
     pages = {357-384},
     doi = {10.1016/j.anihpc.2011.02.002},
     mrnumber = {2795711},
     zbl = {1217.35176},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2011__28_3_357_0}
}

Perelman, Galina. Two soliton collision for nonlinear Schrödinger equations in dimension 1. Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) pp. 357-384. doi : 10.1016/j.anihpc.2011.02.002. http://gdmltest.u-ga.fr/item/AIHPC_2011__28_3_357_0/

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