Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New findings for the old problem: Exact solutions for domain walls in
  coupled real Ginzburg-Landau equations   This work reports new exact solutions for domain-wall (DW) states produced by
a system of coupled real Ginzburg-Landau (GL) equations which model patterns in
thermal convection, optics, and Bose-Einstein condensates (BECs). An exact
solution for symmetric DW was known for a single value of the cross-interaction
coefficient, G = 3 (defined so that its self-interaction counterpart is 1).
Here an exact asymmetric DW is obtained for the system in which the diffusion
term is absent in one component. It exists for all G > 1. Also produced is an
exact solution for DW in the symmetric real-GL system which includes linear
coupling. In addition, an effect of a trapping potential on the DW is
considered, which is relevant to the case of BEC. In a system of three GL
equations, an exact solution is obtained for a composite state including a
two-component DW and a localized state in the third component. Bifurcations
which create two lowest composite states are identified too. Lastly, exact
solutions are found for the system of real GL equations for counterpropagating
waves, which represent a sink or source of the waves, as well as for a system
of three equations which includes a standing localized component.

14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th