Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the non-integrability of the Popowicz peakon system   We consider a coupled system of Hamiltonian partial differential equations
introduced by Popowicz, which has the appearance of a two-field coupling
between the Camassa-Holm and Degasperis-Procesi equations. The latter equations
are both known to be integrable, and admit peaked soliton (peakon) solutions
with discontinuous derivatives at the peaks. A combination of a reciprocal
transformation with Painlev\'e analysis provides strong evidence that the
Popowicz system is non-integrable. Nevertheless, we are able to construct exact
travelling wave solutions in terms of an elliptic integral, together with a
degenerate travelling wave corresponding to a single peakon. We also describe
the dynamics of N-peakon solutions, which is given in terms of an Hamiltonian
system on a phase space of dimension 3N.

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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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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: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: math
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con