Two soliton collision for nonlinear Schrödinger equations in dimension 1
Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 3, pp. 357-384
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We study the collision of two solitons for the nonlinear Schrödinger equation , as , 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: .
@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},
pages = {357--384},
publisher = {Elsevier},
volume = {28},
number = {3},
year = {2011},
doi = {10.1016/j.anihpc.2011.02.002},
mrnumber = {2795711},
zbl = {1217.35176},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2011.02.002/}
}
TY - JOUR AU - Perelman, Galina TI - Two soliton collision for nonlinear Schrödinger equations in dimension 1 JO - Annales de l'I.H.P. Analyse non linéaire PY - 2011 SP - 357 EP - 384 VL - 28 IS - 3 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2011.02.002/ DO - 10.1016/j.anihpc.2011.02.002 LA - en ID - AIHPC_2011__28_3_357_0 ER -
%0 Journal Article %A Perelman, Galina %T Two soliton collision for nonlinear Schrödinger equations in dimension 1 %J Annales de l'I.H.P. Analyse non linéaire %D 2011 %P 357-384 %V 28 %N 3 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2011.02.002/ %R 10.1016/j.anihpc.2011.02.002 %G en %F 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) no. 3, pp. 357-384. doi: 10.1016/j.anihpc.2011.02.002
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