Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High-order soliton matrix for the third-order flow equation of the
  Gerdjikov-Ivanov hierarchy through the Riemann-Hilbert method   The Gerdjikov-Ivanov (GI) hierarchy is derived via recursion operator, in
this paper, we mainly consider the third-order flow GI equation. In the
framework of the Riemann-Hilbert method, through a standard dressing procedure,
soliton matrices for simple zeros and elementary high-order zeros in the
Riemann-Hilbert problem (RHP) for the third-order flow GI equation are
constructed. Taking advantage of this result, some properties and asymptotic
analysis of single soliton solutions and two-soliton solutions are discussed,
and the simple elastic interaction of two-soliton is proved. Compared with
soliton solution of the classical second-order flow, we found that the
higher-order dispersion term affects the propagation velocity, propagation
direction and amplitude of the soliton. Finally, by means of certain limit
technique, the high-order soliton solution matrix for the third-order flow GI
equation is derived.

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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org