Lax representation with spectral parameter on a torus for integrable particle systems

Complete integrability is proved for the most general class of systems of interacting particles on a straight line with the Hamiltonian including elliptic functions of coordinates, depending on seven arbitrary parameters and having the structure defined by the root systems of the classical Lie algebras. The Lax representation for them depends on the spectral parameter given on a complex torus ℂ/г, where Γ is the lattice of periods of the Jacobi functions dependent on the Hamiltonian parameters. The possibility of constructing explicit solutions to the equations of motion is discussed.

Authors and Affiliations

1. Laboratory of Theoretical Physics, JINR, Head Post Office, P.O. Box 79, Moscow, U.S.S.R.

   V. I. Inozemtsev

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