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Grassmann extensions of Yang-Baxter maps

Grahovski, GG and Konstantinou-Rizos, S and Mikhailov, AV (2016) 'Grassmann extensions of Yang-Baxter maps.' Journal of Physics A: Mathematical and Theoretical, 49 (14). ISSN 1751-8113

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Abstract

© 2016 IOP Publishing Ltd. In this paper we show that there are explicit Yang-Baxter (YB) maps with Darboux-Lax representation between Grassman extensions of algebraic varieties. Motivated by some recent results on noncommutative extensions of Darboux transformations, we first derive a Darboux matrix associated with the Grassmann-extended derivative nonlinear Schrödinger (DNLS) equation, and then we deduce novel endomorphisms of Grassmann varieties, which possess the YB property. In particular, we present ten-dimensional maps which can be restricted to eight-dimensional YB maps on invariant leaves, related to the Grassmann-extended NLS and DNLS equations. We consider their vector generalisations.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Jim Jamieson
Date Deposited: 07 Apr 2016 11:58
Last Modified: 23 Jan 2019 00:16
URI: http://repository.essex.ac.uk/id/eprint/16379

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