Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stable and chaotic solutions of the complex Ginzburg-Landau equation
  with periodic boundary conditions   We study, analytically and numerically, the dynamical behavior of the
solutions of the complex Ginzburg-Landau equation with diffraction but without
diffusion, which governs the spatial evolution of the field in an active
nonlinear laser cavity. Accordingly, the solutions are subject to periodic
boundary conditions. The analysis reveals regions of stable stationary
solutions in the model&#8217;s parameter space, and a wide range of oscillatory
and chaotic behaviors. Close to the first bifurcation destabilizing the
spatially uniform solution, a stationary single-humped solution is found in an
asymptotic analytical form, which turns out to be in very good agreement with
the numerical results. Simulations reveal a series of stable stationary
multi-humped solutions

23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
2
The categories of this paper are: math
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph