Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Darboux transformation and higher-order rogue wave solutions
  of the coupled Hirota equations   This paper is dedicated to study higher-order rogue wave solutions of the
coupled Hirota equations with high-order nonlinear effects like the third
dispersion, self-steepening and stimulated Raman scattering terms. By using the
generalized Darboux transformation, a unified representation of Nth-order rogue
wave solution with 3N+1 free parameters is obtained. In particular, the
first-order rogue wave solution containing polynomials of fourth order, and the
second-order rogue wave solution consisting of polynomials of eighth order are
explicitly presented. Through the numerical plots, we show that four or six
fundamental rogue waves can coexist in the second-order rogue waves. By
adjusting the values of some free parameters, different kinds of
spatial-temporal distribution structures such as circular, quadrilateral,
triangular, line and fundamental patterns are exhibited. Moreover, we see that
nine or twelve fundamental rogue waves can synchronously emerge in the
third-order rogue waves. The more intricate spatialtemporal distribution shapes
are shown via adequate choices of the free parameters. Several wave
characteristics such as the amplitudes and the coordinate positions of the
highest peaks in the rogue waves are discussed.

28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat