Two soliton collision for nonlinear Schrödinger equations in dimension 1
Galina Perelman
Université Paris-Est, Laboratoire dʼAnalyse et de Mathématiques Appliquées, 61 avenue du Général de Gaulle, 94010 Créteil, France
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Abstract
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: .
Cite this article
Galina Perelman, Two soliton collision for nonlinear Schrödinger equations in dimension 1. Ann. Inst. H. Poincaré Anal. Non Linéaire 28 (2011), no. 3, pp. 357–384
DOI 10.1016/J.ANIHPC.2011.02.002