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• W3105367392 abstract "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$_r$,($rgeq 3$) extension is briefly discussed in this approach. The properties and calculations of some matrix elements using level one vertex operators are outlined." @default.
• W3105367392 created "2020-11-23" @default.
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• W3105367392 date "2012-02-09" @default.
• W3105367392 modified "2023-10-09" @default.
• W3105367392 title "New derivation of soliton solutions to the AKNS2system via dressing transformation methods" @default.
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• W3105367392 doi "https://doi.org/10.1088/1751-8113/45/8/085205" @default.
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