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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). p. 145202. ISSN 1751-8113

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Abstract

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
Additional Information: 18 pages, LaTeX
Uncontrolled Keywords: Yang-Baxter maps; Grassmann algebraic varieties; Grassmann extensions of Yang-Baxter maps; Grassmann extensions of Darboux transformations; noncommutative extensions of Yang-Baxter maps
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: 07 Apr 2016 11:58
Last Modified: 15 Jan 2022 00:27
URI: http://repository.essex.ac.uk/id/eprint/16379

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