Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variational derivation of two-component Camassa-Holm shallow water
  system   By a variational approach in the Lagrangian formalism, we derive the
nonlinear integrable two-component Camassa-Holm system (1). We show that the
two-component Camassa-Holm system (1) with the plus sign arises as an
approximation to the Euler equations of hydrodynamics for propagation of
irrotational shallow water waves over a flat bed. The Lagrangian used in the
variational derivation is not a metric.

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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci