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arXiv · 1510.06913

Grassmann extensions of Yang-Baxter maps

Georgi G. Grahovski·Sotiris Konstantinou-Rizos·Alexander V. Mikhailov
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Abstract

In this paper we show that there are explicit Yang-Baxter maps with Darboux-Lax representation between Grassmann 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 Schrodinger (DNLS) equation, and then we deduce novel endomorphisms of Grassmann varieties, which possess the Yang-Baxter property. In particular, we present ten-dimensional maps which can be restricted to eight-dimensional Yang-Baxter maps on invariant leaves, related to the Grassmann-extended NLS and DNLS equations. We consider their vector generalisations.

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Georgi G. Grahovski, Sotiris Konstantinou-Rizos, Alexander V. Mikhailov. 2016-02-23. Grassmann extensions of Yang-Baxter maps. https://doi.org/10.1088/1751-8113%2F49%2F14%2F145202

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