Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear and Nonlinear PT-symmetric Oligomers: A Dynamical Systems
  Analysis   In the present work we focus on the cases of two-site (dimer) and three-site
(trimer) configurations, i.e. oligomers, respecting the parity-time (PT)
symmetry, i.e., with a spatially odd gain-loss profile. We examine different
types of solutions of such configurations with linear and nonlinear gain/loss
profiles. Solutions beyond the linear PT-symmetry critical point as well as
solutions with asymmetric linearization eigenvalues are found in both the
nonlinear dimer and trimer. The latter feature is absent in linear PT-symmetric
trimers, while both of them are absent in linear PT symmetric dimers.
Furthermore, nonlinear gain/loss terms enable the existence of both symmetric
and asymmetric solution profiles (and of bifurcations between them), while only
symmetric solutions are present in the linear PT-symmetric dimers and trimers.
The linear stability analysis around the obtained solutions is discussed and
their dynamical evolution is explored by means of direct numerical simulations.
Finally, a brief discussion is also given of recent progress in the context of
PT-symmetric quadrimers.

2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th