Výsledky vyhledávání - "Atalikov, K."

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Gauge equivalence of 1+1 Calogero-Moser-Sutherland field theory and higher rank trigonometric Landau-Lifshitz model

Autor: Atalikov, K., Zotov, A.

Publikováno v: Theoret. and Math. Phys., 219:3 (2024), 1004-1017

We consider the classical integrable 1+1 trigonometric ${\rm gl}_N$ Landau-Lifshitz models constructed by means of quantum $R$-matrices satisfying also the associative Yang-Baxter equation. It is shown that 1+1 field analogue of the trigonometric Cal

Externí odkaz: http://arxiv.org/abs/2403.00428

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Gauge equivalence between 1+1 rational Calogero-Moser field theory and higher rank Landau-Lifshitz equation

Autor: Atalikov, K., Zotov, A.

Publikováno v: Jetp Lett. 117, 630-634 (2023)

In this paper we study 1+1 field generalization of the rational $N$-body Calogero-Moser model. We show that this model is gauge equivalent to some special higher rank matrix Landau-Lifshitz equation. The latter equation is described in terms of ${\rm

Externí odkaz: http://arxiv.org/abs/2303.08020

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Higher rank generalization of 11-vertex rational R-matrix: IRF-Vertex relations and associative Yang-Baxter equation

Autor: Atalikov, K., Zotov, A.

Publikováno v: Theoret. and Math. Phys., 216:2 (2023) 1083-1103

We study ${\rm GL}_N$ rational $R$-matrix, which turns into the 11-vertex $R$-matrix in the $N=2$ case. First, we describe its relations to dynamical and semi-dynamical $R$-matrices using the IRF-Vertex type transformations. As a by-product a new exp

Externí odkaz: http://arxiv.org/abs/2303.02391

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Higher rank 1+1 integrable Landau-Lifshitz field theories from associative Yang-Baxter equation

Autor: Atalikov, K., Zotov, A.

Publikováno v: Jetp Lett. 115, 757-762 (2022)

We propose a construction of 1+1 integrable Heisenberg-Landau-Lifshitz type equations in the ${\rm gl}_N$ case. The dynamical variables are matrix elements of $N\times N$ matrix $S$ with the property $S^2={\rm const}\cdot S$. The Lax pair with spectr

Externí odkaz: http://arxiv.org/abs/2204.12576

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Field theory generalizations of two-body Calogero-Moser models in the form of Landau-Lifshitz equations

Autor: Atalikov, K., Zotov, A.

Publikováno v: J. Geom. Phys., 164 (2021) 104161

We give detailed description for continuous version of the classical IRF-Vertex relation, where on the IRF side we deal with the Calogero-Moser-Sutherland models. Our study is based on constructing modifications of the Higgs bundles of infinite rank

Externí odkaz: http://arxiv.org/abs/2010.14297

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