Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The N-soliton solution of the Degasperis-Procesi equation   This paper extends the results of the previous paper designated I hereafter
in which the one- and two-soiton solutions of the Degasperis-Procesi(DP)
equation were obtained and their peakon limit was considered. Here, we present
the general N-soliton solution of the DP equation and investigate its property.
We show that it has a novel structure expressed by a parametric representation
in terms of the BKP tau-functions. A purely algebraic proof of the solution is
given by establishing various identities among the tau-functions. The large
time asymptotic of the solution recovers the formula for the phase shift which
was derived in I by a different method. Finally, the structure of the N-soliton
solution is discussed in comparison with that of the Camassa-Holm shallow water
wave equation.

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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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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: hep-lat
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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: hep-th
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The categories of this paper are: q-bio