Integrable Discretisations for a Class of Nonlinear Schrodinger Equations on Grassmann Algebras

Integrable discretisations for a class of coupled (super) nonlinear Schrodinger (NLS) type of equations are presented. The class corresponds to a Lax operator with entries in a Grassmann algebra. Elementary Darboux transformations are constructed. As a result, Grassmann generalisations of the Toda l...

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Bibliographic Details
Published in:arXiv.org 2014-05
Main Authors: Grahovski, Georgi G, Mikhailov, Alexander V
Format: Article
Language:English
Subjects:
Commutativity
Discrete systems
Mathematical analysis
Nonlinear equations
Schrodinger equation
Transformations (mathematics)
Vector spaces
Online Access:Get full text
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Summary:Integrable discretisations for a class of coupled (super) nonlinear Schrodinger (NLS) type of equations are presented. The class corresponds to a Lax operator with entries in a Grassmann algebra. Elementary Darboux transformations are constructed. As a result, Grassmann generalisations of the Toda lattice and the NLS dressing chain are obtained. The compatibility (Bianchi commutativity) of these Darboux transformations leads to integrable Grassmann generalisations of the difference Toda and NLS equations. The resulting systems will have discrete Lax representations provided by the set of two consistent elementary Darboux transformations. For the two discrete systems obtained, initial value and initialboundary problems are formulated.
ISSN:2331-8422
DOI:10.48550/arxiv.1303.1853