Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Darboux transformation of the second-type derivative nonlinear
  Schr\"odinger equation   The second-type derivative nonlinear Schr\"odinger (DNLSII) equation was
introduced as an integrable model in 1979. Very recently, the DNLSII equation
has been shown by an experiment to be a model of the evolution of optical
pulses involving self-steepening without concomitant self-phase-modulation. In
this paper the $n$-fold Darboux transformation (DT) $T_n$ of the coupled DNLSII
equations is constructed in terms of determinants. Comparing with the usual DT
of the soliton equations, this kind of DT is unusual because $T_n$ includes
complicated integrals of seed solutions in the process of iteration. By a
tedious analysis, these integrals are eliminated in $T_n$ except the integral
of the seed solution. Moreover, this $T_n$ is reduced to the DT of the DNLSII
equation under a reduction condition. As applications of $T_n$, the explicit
expressions of soliton, rational soliton, breather, rogue wave and multi-rogue
wave solutions for the DNLSII equation are displayed.

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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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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: nucl-th
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The categories of this paper are: q-bio