Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orbit Approach to Separation of Variables in sl(3)-Related Integrable
  Systems   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 Schr\"{o}dinger
equation and an isotropic SU(3) Landau-Lifshitz equation.

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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
1
The categories of this paper are: cs
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The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc