Orbit Approach to Separation of Variables in sl(4)-Related Integrable Systems

Abstract

Separation of variables by means of the orbit method is implemented to integrable systems on coadjoint orbits in an $\mathfrak{sl}(4)$ loop algebra. This is a development and a kind of explanation for Sklyanin's procedure of separation of variables. It is shown that points on a spectral curve serve as variables of separation for two integrable systems living on two generic orbits embedded into a common manifold. These orbits are endowed with different nonsingular Lie-Poisson brackets. Explicit expressions for the case of $\mathfrak{sl}(4)$ loop algebra are given.

12 pages. arXiv admin note: substantial text overlap with arXiv:1312.1975

References in corpus (3)

• A generalised Landau-Lifshitz equation for isotropic SU(3) magnet
• Multi-Hamiltonian structures for r-matrix systems
• On Separation of Variables for Integrable Equations of Soliton Type