Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Domain walls in the coupled Gross-Pitaevskii equations with the harmonic
  potential   We study the existence and variational characterization of steady states in a
coupled system of Gross--Pitaevskii equations modeling two-component
Bose-Einstein condensates with the magnetic field trapping. The limit with no
trapping has been the subject of recent works where domain walls have been
constructed and several properties, including their orbital stability have been
derived. Here we focus on the full model with the harmonic trapping potential
and characterize minimizers according to the value of the coupling parameter
$\gamma$. We first establish a rigorous connection between the two problems in
the Thomas-Fermi limit via $\Gamma$-convergence. Then, we identify the ranges
of $\gamma$ for which either the symmetric states $(\gamma < 1)$ or the
uncoupled states $(\gamma > 1)$ are minimizers. Domain walls arise as
minimizers in a subspace of the energy space with a certain symmetry for some
$\gamma > 1$. We study bifurcation of the domain walls and furthermore give
numerical illustrations of our results.

34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg