Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A connection between the shallow-water equations and the
  Euler-Poincar\'e equations   The Euler-Poincar\'e differential (EPDiff) equations and the shallow water
(SW) equations share similar wave characteristics. Using the Hamiltonian
structure of the SW equations with flat bottom topography, we establish a
connection between the EPDiff equations and the SW equations in one and
multi-dimensions. Additionally, we show that the EPDiff equations can be recast
in a curl formulation.

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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph