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Integrable discretisations for a class of nonlinear Schrödinger equations on Grassmann algebras

Grahovski, Georgi G and Mikhailov, Alexander V (2013) 'Integrable discretisations for a class of nonlinear Schrödinger equations on Grassmann algebras.' Physics Letters A, 377 (45-48). pp. 3254-3259. ISSN 0375-9601

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Abstract

Integrable discretisations for a class of coupled (super) nonlinear Schrödinger (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 initial-boundary problems are formulated. © 2013 Elsevier B.V. All rights reserved.

Item Type: Article
Additional Information: 12 pages, LaTeX
Uncontrolled Keywords: nlin.SI; hep-th; math-ph; math.MP
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 12 Nov 2014 12:50
Last Modified: 18 Aug 2022 11:28
URI: http://repository.essex.ac.uk/id/eprint/11523

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