Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: General rogue waves and their dynamics in several reverse time
  integrable nonlocal nonlinear equations   A study of general rogue waves in some integrable reverse time nonlocal
nonlinear equations is presented. Specifically, the reverse time nonlocal
nonlinear Schr\"odinger (NLS) and nonlocal Davey-Stewartson (DS) equations are
investigated, which are nonlocal reductions from the AKNS hierarchy. By using
Darboux transformation (DT) method, several types of rogue waves are
constructed. Especially, a unified binary DT is found for this nonlocal DS
system, thus the solution formulas for nonlocal DSI and DSII equation can be
written in an uniform expression. Dynamics of these rogue waves is separately
explored. It is shown that the (1+1)-dimensional rogue waves in nonlocal NLS
equation can be bounded for both x and t, or develop collapsing singularities.
It is also shown that the (1+2)-dimensional line rogue waves in the nonlocal DS
equations can be bounded for all space and time, or have finite-time
blowing-ups. All these types depend on the values of free parameters introduced
in the solution. In addition, the dynamics patterns in the multi- and
higher-order rogue waves exhibits more richer structures, most of which have no
counterparts in the corresponding local nonlinear equations.

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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: math
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th