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

Abstract

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 ${\mathrm{GL}}_N$ rational $R$-matrix, which turns into the 11-vertex $R$-matrix in the $N=2$ case. The rational $R$-matrix satisfies the associative Yang-Baxter equation, which underlies construction of the Lax pair for the Zakharov-Shabat equation. The field analogue of the IRF-Vertex transformation is proposed. It allows to compute explicit change of variables between the field Calogero-Moser model and the Landau-Lifshitz equation.

7 pages, minor corrections

References in corpus (4)

• Relativistic Classical Integrable Tops and Quantum R-matrices
• Classical integrable systems and soliton equations related to eleven-vertex R-matrix
• Field analogue of the Ruijsenaars-Schneider model
• Higher rank 1+1 integrable Landau-Lifshitz field theories from associative Yang-Baxter equation

Cited by in corpus (3)

• Non-ultralocal classical r-matrix structure for 1+1 field analogue of elliptic Calogero-Moser model
• On the field analogue of elliptic spin Calogero-Moser model: Lax pair and equations of motion
• Gauge equivalence of 1+1 Calogero-Moser-Sutherland field theory and higher rank trigonometric Landau-Lifshitz model