Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The direct scattering study of the parametrically driven nonlinear
  Schr\"odinger equation   The term "direct scattering study" refers to the calculation and analysis of
the discrete eigenvalues of the associated Zakharov-Shabat (ZS) eigenvalue
problem. The direct scattering study was applied to time-dependent oscillating
solitons that arise as attractors in the parametrically driven nonlinear
Schr\"odinger equation. Four different types of attractors within the parameter
space are identified, each with a unique soliton content structure. These
structures include radiation-induced nonlinear modes and soliton complex
structures. The different types of attractors are used to characterise the
dependence of the attractors on damping and driving parameters. Period-doubling
bifurcations are shown to affect the radiation emissions of oscillating
solitons. The role of soliton complex structures and radiation in the formation
of spatio-temporal chaos is also identified.

17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg