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Orbit Approach to Separation of Variables in \({\mathfrak{sl}}\)(3)-Related Integrable Systems

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Abstract

Using the orbit method we reveal geometric and algebraic meaning of separation of variables for integrable systems on coadjoint orbits of 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 integrable systems on the orbits: a coupled 3-component nonlinear Schrödinger equation and an isotropic SU(3) Landau–Lifshitz equation.

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Authors and Affiliations

  1. National University of ‘Kyiv Mohyla Academy’, G. Skovorody st., 2, Kiev, 04655, Ukraine

    Julia Bernatska & Petro Holod

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  1. Julia Bernatska
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  2. Petro Holod
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Correspondence to Julia Bernatska.

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Communicated by N. Reshetikhin

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Bernatska, J., Holod, P. Orbit Approach to Separation of Variables in \({\mathfrak{sl}}\)(3)-Related Integrable Systems. Commun. Math. Phys. 333, 905–929 (2015). https://doi.org/10.1007/s00220-014-2176-9

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  • DOI: https://doi.org/10.1007/s00220-014-2176-9

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