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arXiv · 1312.1975

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

Julia Bernatska·Petro Holod
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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.

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Julia Bernatska, Petro Holod. 2014-08-16. Orbit Approach to Separation of Variables in sl(3)-Related Integrable Systems. https://doi.org/10.1007/s00220-014-2176-9

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