Generalized model of interacting integrable tops

Abstract

We introduce a family of classical integrable systems describing dynamics of $M$ interacting ${\mathrm{gl}}_N$ integrable tops. It extends the previously known model of interacting elliptic tops. Our construction is based on the ${\mathrm{GL}}_N$ $R$-matrix satisfying the associative Yang-Baxter equation. The obtained systems can be considered as extensions of the spin type Calogero-Moser models with (the classical analogues of) anisotropic spin exchange operators given in terms of the $R$-matrix data. In $N=1$ case the spin Calogero-Moser model is reproduced. Explicit expressions for ${\mathrm{gl}}_{NM}$-valued Lax pair with spectral parameter and its classical dynamical $r$-matrix are obtained. Possible applications are briefly discussed.

30 pages, minor changes

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Cited by in corpus (12)

• Field analogue of the Ruijsenaars-Schneider model
• Higher rank 1+1 integrable Landau-Lifshitz field theories from associative Yang-Baxter equation
• Anisotropic spin generalization of elliptic Macdonald-Ruijsenaars operators and R-matrix identities
• GL(NM) quantum dynamical $R$-matrix based on solution of the associative Yang-Baxter equation
• Elliptic generalization of integrable q-deformed anisotropic Haldane-Shastry long-range spin chain
• Integrable System of Generalized Relativistic Interacting Tops
• Relativistic interacting integrable elliptic tops
• Classical integrable spin chains of Landau-Lifshitz type from R-matrix identities
• Integrable systems on multiplicative quiver varieties from cyclic quivers
• Multi-pole extension for elliptic models of interacting integrable tops
• On R-matrix identities related to elliptic anisotropic spin Ruijsenaars-Macdonald operators
• R-matrix valued Lax pair for elliptic Calogero-Inozemtsev system and associative Yang-Baxter equations of ${\mathrm{BC}}_n$ type