Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Integrable Shallow Water Equation with Linear and Nonlinear
  Dispersion   We study a class of 1+1 quadratically nonlinear water wave equations that
combines the linear dispersion of the Korteweg-deVries (KdV) equation with the
nonlinear/nonlocal dispersion of the Camassa-Holm (CH) equation, yet still
preserves integrability via the inverse scattering transform (IST) method.
  This IST-integrable class of equations contains both the KdV equation and the
CH equation as limiting cases. It arises as the compatibility condition for a
second order isospectral eigenvalue problem and a first order equation for the
evolution of its eigenfunctions. This integrable equation is shown to be a
shallow water wave equation derived by asymptotic expansion at one order higher
approximation than KdV. We compare its traveling wave solutions to KdV
solitons.

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The categories of this paper are: stat
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The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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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: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph