arXiv 0804.03952008-04math.APmath-phmath.MP

Fast soliton scattering by attractive delta impurities

Kiril Datchev, Justin Holmer

发表信息：: Communications in Partial Differential Equations, Vol. 34, No. 9, pp. 1074-1113, 2009
DOI：: 10.1080/03605300903076831

英文摘要：

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.

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