Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multistable Solitons in the Cubic-Quintic Discrete Nonlinear
  Schr\"odinger Equation   We analyze the existence and stability of localized solutions in the
one-dimensional discrete nonlinear Schr\"{o}dinger (DNLS) equation with a
combination of competing self-focusing cubic and defocusing quintic onsite
nonlinearities. We produce a stability diagram for different families of
soliton solutions, that suggests the (co)existence of infinitely many branches
of stable localized solutions. Bifurcations which occur with the increase of
the coupling constant are studied in a numerical form. A variational
approximation is developed for accurate prediction of the most fundamental and
next-order solitons together with their bifurcations. Salient properties of the
model, which distinguish it from the well-known cubic DNLS equation, are the
existence of two different types of symmetric solitons and stable asymmetric
soliton solutions that are found in narrow regions of the parameter space. The
asymmetric solutions appear from and disappear back into the symmetric ones via
loops of forward and backward pitchfork bifurcations.

16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio