Relativistic interacting integrable elliptic tops

Abstract

We propose relativistic generalization of integrable systems describing $M$ interacting elliptic $\mathrm{gl}(N)$ tops of the Euler-Arnold type. The obtained models are elliptic integrable systems, which reproduce the spin elliptic $\mathrm{GL}(M)$ Ruijsenaars-Schneider model for $N=1$ case, while in the $M=1$ case they turn into relativistic integrable $\mathrm{GL}(N)$ elliptic tops. The Lax pairs with spectral parameter on elliptic curve are constructed.

17 pages

References in corpus (4)

• Physics and Mathematics of Calogero particles
• Relativistic Classical Integrable Tops and Quantum R-matrices
• Relativistic elliptic matrix tops and finite Fourier transformations
• Quantum Trace Formulae for the Integrals of the Hyperbolic Ruijsenaars-Schneider model