Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a two-component $\pi$-Camassa--Holm system   A novel $\pi$-Camassa--Holm system is studied as a geodesic flow on a
semidirect product obtained from the diffeomorphism group of the circle. We
present the corresponding details of the geometric formalism for metric Euler
equations on infinite-dimensional Lie groups and compare our results to what
has already been obtained for the usual two-component Camassa--Holm equation.
Our approach results in well-posedness theorems and explicit computations of
the sectional curvature.

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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int