Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher-order rogue wave dynamics for a derivative nonlinear
  Schr\"odinger equation   The the mixed Chen-Lee-Liu derivative nonlinear Schr\"odinger equation
(CLL-NLS) can be considered as simplest model to approximate the dynamics of
weakly nonlinear and dispersive waves, taking into account the self-steepnening
effect (SSE). The latter effect arises as a higher-order correction of the
nonlinear Schr\"ordinger equation (NLS), which is known to describe the
dynamics of pulses in nonlinear fiber optics, and constiutes a fundamental part
of the generalized NLS. Similar effects are decribed within the framework of
the modified NLS, also referred to as the Dysthe equation, in hydrodynamics. In
this work, we derive fundamental and higher-order solutions of the CLL-NLS by
applying the Darboux transformation (DT). Exact expressions of non-vanishing
boundary solitons, breathers and a hierarchy of rogue wave solutions are
presented. In addition, we discuss the localization characters of such rogue
waves, by characterizing their length and width. In particular, we describe how
the localization properties of first-order NLS rogue waves can be modified by
taking into account the SSE, presented in the CLL-NLS. This is illustrated by
use of an analytical and a graphical method. The results may motivate similar
analytical studies, extending the family of the reported rogue wave solutions
as well as possible experiments in several nonlinear dispersive media,
confirming these theoretical results.

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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn