Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poisson Pencils, Integrability, and Separation of Variables   In this paper we will review a recently introduced method for solving the
Hamilton-Jacobi equations by the method of Separation of Variables. This method
is based on the notion of pencil of Poisson brackets and on the bihamiltonian
approach to integrable systems. We will discuss how separability conditions can
be intrinsically characterized within such a geometrical set-up, the definition
of the separation coordinates being encompassed in the \bih structure itself.
We finally discuss these constructions studying in details a particular
example, based on a generalization of the classical Toda Lattice.

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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: econ