no. 3
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

We study the collision of two solitons for the nonlinear Schrödinger equation iψ t =-ψ xx +F(|ψ| 2 )ψ, F(ξ)=-2ξ+O(ξ 2 ) as ξ→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: iψ t =-ψ xx -2|ψ| 2 ψ.

@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},
     year = {2011},
     publisher = {Elsevier},
     volume = {28},
     number = {3},
     doi = {10.1016/j.anihpc.2011.02.002},
     mrnumber = {2795711},
     zbl = {1217.35176},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2011.02.002/}
}
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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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