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Title: | Soliton resonances in a generalized nonlinear Schrödinger equation | Authors: | Pashaev, Oktay Lee, Jyh Hao Rogers, Colin |
Keywords: | Schrödinger equation Black holes Space-time |
Publisher: | IOP Publishing Ltd. | Source: | Pashaev, O., Lee, J. H., and Rogers, C. (2008). Soliton resonances in a generalized nonlinear Schrödinger equation. Journal of Physics A: Mathematical and Theoretical, 41(45). doi: 10.1088/1751-8113/41/45/452001 | Abstract: | It is shown that a generalized nonlinear Schrödinger equation proposed by Malomed and Stenflo admits, for a specific range of parameters, resonant soliton interaction. The equation is transformed to the 'resonant' nonlinear Schrödinger equation, as originally introduced to describe black holes in a Madelung fluid and recently derived in the context of uniaxial wave propagation in a cold collisionless plasma. A Hirota bilinear representation is obtained and soliton solutions are thereby derived. The one-soliton solution interpretation in terms of a black hole in two-dimensional spacetime is given. For the two-soliton solution, resonant interactions of several kinds are found. The addition of a quantum potential term is considered and the reduction is obtained to the resonant NLS equation. © 2008 IOP Publishing Ltd. | URI: | http://doi.org/10.1088/1751-8113/41/45/452001 http://hdl.handle.net/11147/2142 |
ISSN: | 1751-8113 1751-8121 1751-8113 |
Appears in Collections: | Mathematics / Matematik Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection |
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