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

被引：28
|
作者：
Grahovski, Georgi G. [1 ,2 ]
Mikhailov, Alexander V. [1 ]
机构：
[1] Univ Leeds, Dept Appl Math, Leeds LS2 9JT, W Yorkshire, England
[2] Bulgarian Acad Sci, Inst Nucl Res & Nucl Energy, BU-1784 Sofia, Bulgaria
来源：
PHYSICS LETTERS A | 2013年 / 377卷 / 45-48期
基金：
英国工程与自然科学研究理事会;
关键词：
SUPERSYMMETRIC KDV EQUATION; TODA LATTICE; BACKLUND-TRANSFORMATIONS; DIFFERENCE-EQUATIONS; HIERARCHY; EXTENSION; SYSTEMS; OPERATORS;
D O I：
10.1016/j.physleta.2013.10.018
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
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 initial-boundary problems are formulated. (C) 2013 Elsevier B.V. All rights reserved.
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页码：3254 / 3259
页数：6
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