Orbit Approach to Separation of Variables in sl(3)-Related Integrable Systems

Abstract

Using the orbit method we attempt to reveal geometric and algebraic meaning of separation of variables for the integrable systems on coadjoint orbits in an $\mathfrak{sl}(3)$ loop algebra. We consider two types of generic orbits embedded into a common manifold, endowed with two nonsingular Lie-Poisson brackets. We prove that separation of variables on orbits of both types is realized by the same variables of separation. We also construct the integrable systems on these orbits: a coupled 3-component nonlinear Schrödinger equation and an isotropic SU(3) Landau-Lifshitz equation.

20 pages

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