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- W1900545428 abstract "We consider certain boundary conditions supporting soliton solutions in the generalized non-linear Schrodinger equation (AKNS). 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. 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. 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 Schrodinger equation ($r-$CNLS), which has recently been considered in many physical applications. The properties and calculations of some matrix elements using level one vertex operators are outlined." @default.
- W1900545428 created "2016-06-24" @default.
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- W1900545428 date "2011-10-14" @default.
- W1900545428 modified "2023-10-09" @default.
- W1900545428 title "Generalized AKNS System, Non-vanishing Boundary Conditions and N-Dark-Dark Solitons" @default.
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