Two soliton collision for nonlinear Schrödinger equations in dimension 1
Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 3, p. 357-384

We study the collision of two solitons for the nonlinear Schrödinger equation $i{\psi }_{t}=-{\psi }_{xx}+F\left({|\psi |}^{2}\right)\psi$, $F\left(\xi \right)=-2\xi +O\left({\xi }^{2}\right)$ as $\xi \to 0$, 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: $i{\psi }_{t}=-{\psi }_{xx}-2{|\psi |}^{2}\psi$.

@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},
publisher = {Elsevier},
volume = {28},
number = {3},
year = {2011},
pages = {357-384},
doi = {10.1016/j.anihpc.2011.02.002},
zbl = {1217.35176},
mrnumber = {2795711},
language = {en},
url = {http://www.numdam.org/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, Volume 28 (2011) no. 3, pp. 357-384. doi : 10.1016/j.anihpc.2011.02.002. http://www.numdam.org/item/AIHPC_2011__28_3_357_0/

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