Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two-component gap solitons in two- and one-dimensional Bose-Einstein
  condensates   We introduce 2D and 1D models of a binary Bose-Einstein condensate in a
periodic potential, with repulsive interactions. We chiefly consider the most
fundamental case of the inter-species repulsion with zero intra-species
interactions. Existence and stability regions for gap solitons (GSs) supported
by the interplay of the inter-species repulsion and periodic potential are
identified. Two-component GSs are constructed by means of the variational
approximation (VA) and in a numerical form. The VA provides accurate
description for the GS which is a bound state of two tightly-bound components,
each essentially trapped in one cell of the periodic potential. GSs of this
type dominate in the case of intra-gap solitons, with both components belonging
to the first finite bandgap of the linear spectrum. Inter-gap solitons, with
one component residing in the second bandgap, and intra-gap solitons which have
both components in the second gap, are possible in a deeper periodic potential,
with the strength essentially exceeding the recoil energy of the atoms.
Inter-gap solitons are, typically, bound states of one tightly- and one
loosely-bound components. In this case, results are obtained in a numerical
form. For 2D solitons, the stability is identified in direct simulations, while
in the 1D case it is done via eigenfrequencies of small perturbations, and then
verified by simulations. In the latter case, if the intra-gap soliton in the
first bandgap is weakly unstable, it evolves into a stable breather, while
unstable solitons of other types get completely destroyed. The intra-gap 2D
solitons in the first bandgap are less robust, and in some cases they are
completely destroyed by the instability. Addition of intra-species repulsion to
the repulsion between the components leads to further stabilization of the GSs.

20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
2
The categories of this paper are: math
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ