Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Moving embedded lattice solitons   It was recently proved that isolated unstable "embedded lattice solitons"
(ELS) may exist in discrete systems. The discovery of these ELS gives rise to
relevant questions such as the following: are there continuous families of
ELS?, can ELS be stable?, is it possible for ELS to move along the lattice?,
how do ELS interact?. The present work addresses these questions by showing
that a novel differential-difference equation (a discrete version of a complex
mKdV equation) has a two-parameter continuous family of exact ELS. The
numerical tests reveal that these solitons are stable and robust enough to
withstand collisions. The model may apply to the description of a Bose-Einstein
condensate with dipole-dipole interactions between the atoms, trapped in a deep
optical-lattice potential.

10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol