Monday, March 11, 2013

1303.1853 (Georgi G. Grahovski et al.)

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

Georgi G. Grahovski, Alexander V. Mikhailov
Integrable discretisations for a class of coupled 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 Grassmamm generalisations of the difference Toda and NLS equations. The resulting discrete systems will have Lax pairs provided by the set of two consistent Darboux transformations.
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