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:
Communications in Partial Differential Equations,
Volume
34,
Issue
9
September
2009
, pages 1074
- 1113
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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 Schr dinger equations;
Scattering solitons
|
| Mathematics Subject Classification: 35Q51; 35Q55 |
| view references (7) |

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dinger equations;
Scattering solitons
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