Geodesic
Gauge equivalence of $1+1$ Calogero–Moser–Sutherland field
Teoretičeskaâ i matematičeskaâ fizika, Tome 219 (2024) no. 3, pp. 545-561 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the classical integrable $(1+1)$ trigonometric $gl_N$ Landau–Lifshitz models constructed by means of quantum $R$-matrices that also satisfy the associative Yang–Baxter equation. It is shown that a $(1+1)$ field analogue of the trigonometric Calogero–Moser–Sutherland model is gauge equivalent to the Landau–Lifshitz model that arises from the Antonov–Hasegawa–Zabrodin trigonometric nonstandard $R$-matrix. The latter generalizes Cherednik's $7$-vertex $R$-matrix in the $GL_2$ case to the case of $GL_N$. An explicit change of variables between the $(1+1)$ models is obtained.
Keywords: integrable systems, Landau–Lifshitz equation.
Mots-clés : soliton equations, Calogero–Moser model 
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K. R. Atalikov; A. V. Zotov. Gauge equivalence of $1+1$ Calogero–Moser–Sutherland field. Teoretičeskaâ i matematičeskaâ fizika, Tome 219 (2024) no. 3, pp. 545-561. http://geodesic.mathdoc.fr/item/TMF_2024_219_3_a8/

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