Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orbital Stability of smooth solitary waves for the Degasperis-Procesi
  Equation   The Degasperis-Procesi equation is the integrable Camassa-Holm-type model
which is an asymptotic approximation for the unidirectional propagation of
shallow water waves. This work establishes the orbital stability of localized
smooth solitary waves to the Desgasperis-Procesi (DP) equation on the real
line. %extending our previous work on their spectral stability \cite{LLW}. The
main difficulty stems from the fact that the translation symmetry for the DP
equation gives rise to a conserved quantity equivalent to the $L^2$-norm, which
by itself can not bound the higher-order nonlinear terms in the Lagrangian. The
remedy is to observe that, given a sufficiently smooth initial condition
satisfying a measurable constraint, the $L^\infty$ orbital norm of the
perturbation is bounded above by a function of its $L^2$ orbital norm, yielding
the orbital stability in the $L^2\cap L^\infty$ space.

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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: supr-con