Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rogue waves for a system of coupled derivative nonlinear Schr\"odinger
  equations   Rogue waves (RWs) are unexpectedly strong excitations emerging from an
otherwise tranquil background. The nonlinear Schr\"odinger equation (NLSE), a
ubiquitous model with wide applications to fluid mechanics, optics and plasmas,
exhibits RWs only in the regime of modulation instability (MI) of the
background. For system of multiple waveguides, the governing coupled NLSEs can
produce regimes of MI and RWs, even if each component has dispersion and cubic
nonlinearity of opposite signs. A similar effect will be demonstrated for a
system of coupled derivative NLSEs (DNLSEs), where the special feature is the
nonlinear self-steepening of narrow pulses. More precisely, these additional
regimes of MI and RWs for coupled DNLSEs will depend on the mismatch in group
velocities between the components, as well as the parameters for cubic
nonlinearity and self-steepening. RWs considered in this work differ from those
of the NLSEs in terms of the amplification ratio and criteria of existence.
Applications to optics and plasma physics are discussed.

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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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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: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con