Fast Soliton Scattering by Attractive Delta Impurities |
| |
Authors: | Kiril Datchev |
| |
Institution: | Mathematics Department , University of California , Berkeley, California, USA |
| |
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 Schrödinger equations Scattering solitons |
|
|