New derivation of soliton solutions to the AKNS\(_2\) system via dressing transformation methods
We consider certain boundary conditions supporting soliton solutions in the generalized non-linear Schr\"{o}dinger equation (AKNS\(_r\))\,(\(r=1,2\)). Using the dressing transformation (DT) method and the related tau functions we study the AKNS\(_{r}\) system for the vanishing, (constant) non-v...
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Published in | arXiv.org |
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Main Authors | , , |
Format | Paper |
Language | English |
Published |
Ithaca
Cornell University Library, arXiv.org
28.01.2012
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Subjects | |
Online Access | Get full text |
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Summary: | We consider certain boundary conditions supporting soliton solutions in the generalized non-linear Schr\"{o}dinger equation (AKNS\(_r\))\,(\(r=1,2\)). Using the dressing transformation (DT) method and the related tau functions we study the AKNS\(_{r}\) system for the vanishing, (constant) non-vanishing and the mixed boundary conditions, and their associated bright, dark, and bright-dark N-soliton solutions, respectively. Moreover, we introduce a modified DT related to the dressing group in order to consider the free field boundary condition and derive generalized N-dark-dark solitons. As a reduced submodel of the AKNS\(_r\) system we study the properties of the focusing, defocusing and mixed focusing-defocusing versions of the so-called coupled non-linear Schr\"{o}dinger equation (\(r-\)CNLS), which has recently been considered in many physical applications. We have shown that two\(-\)dark\(-\)dark\(-\)soliton bound states exist in the AKNS\(_2\) system, and three\(-\) and higher\(-\)dark\(-\)dark\(-\)soliton bound states can not exist. The AKNS\(_r\)\,(\(r\geq 3\)) extension is briefly discussed in this approach. The properties and calculations of some matrix elements using level one vertex operators are outlined. |
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ISSN: | 2331-8422 |
DOI: | 10.48550/arxiv.1201.5920 |