Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Smooth and Peaked Solitons of the CH equation   The relations between smooth and peaked soliton solutions are reviewed for
the Camassa-Holm (CH) shallow water wave equation in one spatial dimension. The
canonical Hamiltonian formulation of the CH equation in action-angle variables
is expressed for solitons by using the scattering data for its associated
isospectral eigenvalue problem, rephrased as a Riemann-Hilbert problem. The
momentum map from the action-angle scattering variables $T^*({\mathbb{T}^N})$
to the flow momentum ($\mathfrak{X}^*$) provides the Eulerian representation of
the $N$-soliton solution of CH in terms of the scattering data and squared
eigenfunctions of its isospectral eigenvalue problem. The dispersionless limit
of the CH equation and its resulting peakon solutions are examined by using an
asymptotic expansion in the dispersion parameter. The peakon solutions of the
dispersionless CH equation in one dimension are shown to generalize in higher
dimensions to peakon wave-front solutions of the EPDiff equation whose
associated momentum is supported on smoothly embedded subspaces. The Eulerian
representations of the singular solutions of both CH and EPDiff are given by
the (cotangent-lift) momentum maps arising from the left action of the
diffeomorphisms on smoothly embedded subspaces.

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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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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: cs
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The categories of this paper are: atom-ph