Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multisoliton solutions of the two-component Camassa-Holm system and
  their reductions   We develop a systematic procedure for constructing soliton solutions of an
integrable two-component Camassa-Holm (CH2) system. The parametric
representation of the multisoliton solutions is obtained by using a direct
method combined with a reciprocal transformation. The properties of the
solutions are then investigated in detail focusing mainly on the smooth one-
and two-soliton solutions. The general $N$-soliton case is described shortly.
Subsequently, we show that the CH2 system reduces to the CH equation and the
two-component Hunter-Saxton (HS2) system by means of appropriate limiting
procedures. The corresponding expressions of the multisoliton solutions are
presented in parametric forms, reproducing the existing results for the reduced
equations. Last, we discuss the reduction from the HS2 system to the HS
equation.

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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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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: dg-ga