Fast Soliton Scattering by Attractive Delta Impurities

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 trans...

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Bibliographic Details
Published in:Communications in partial differential equations 2009-08, Vol.34 (9), p.1074-1113
Main Authors: Datchev, Kiril, Holmer, Justin
Format: Article
Language:English
Subjects:
Delta potential
Nonlinear Schrödinger equations
Scattering solitons
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Summary: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.
ISSN:0360-5302
1532-4133
DOI:10.1080/03605300903076831