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Fast Soliton Scattering by Attractive Delta Impurities 

Authors: Kiril Datchev a; Justin Holmer b
Affiliations:   a Mathematics Department, University of California, Berkeley, California, USA
b Mathematics Department, Brown University, Providence, Rhode Island, USA
DOI: 10.1080/03605300903076831
Publication Frequency: 12 issues per year
Published in: journal Communications in Partial Differential Equations, Volume 34, Issue 9 September 2009 , pages 1074 - 1113
Formats available: HTML (English) : PDF (English)
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Abstract

We study the Gross-Pitaevskii equation with an attractive delta function potential and show that in the high velocity limit an incident soliton is split into reflected and transmitted soliton components plus a small amount of dispersion. We give explicit analytic formulas for the reflected and transmitted portions, while the remainder takes the form of an error. Although the existence of a bound state for this potential introduces difficulties not present in the case of a repulsive potential, we show that the proportion of the soliton which is trapped at the origin vanishes in the limit.
Keywords: Delta potential; Nonlinear Schroumldinger equations; Scattering solitons
Mathematics Subject Classification: 35Q51; 35Q55
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