Field generalization of elliptic Calogero-Moser system in the form of higher rank Landau-Lifshitz model

2025/06/01 by K. Atalikov, A. Zotov, Atalikov, K. +1
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Algebraic structures and combinatorial models #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2506.00938

Abstract

We prove gauge equivalence between integrable field generalization of the elliptic Calogero-Moser model and the higher rank XYZ Landau-Lifshitz model of vector type on 1+1 dimensional space-time. Explicit formulae for the change of variables are derived, thus providing the Poisson map between these models.

Citations

• Integrable deformations of principal chiral model from solutions of associative Yang-Baxter equation
• Field theory generalizations of two-body Calogero–Moser models in the form of Landau–Lifshitz equations
• On factorized Lax pairs for classical many-body integrable systems
• Elliptic Families of Solutions of the Kadomtsev-Petviashvili Equation and the Field Elliptic Calogero-Moser System
• Eight-vertex model in lattice statistics and one-dimensional anisotropic heisenberg chain. II. Equivalence to a generalized ice-type lattice model

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• An Explicit Characterization of Calogero--Moser Systems