Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability boundaries and collisions of two-dimensional solitons in
  PT-symmetric couplers with the cubic-quintic nonlinearity   We introduce one- and two-dimensional (1D and 2D) models of parity-time ($%
\mathcal{PT}$) -symmetric couplers with the mutually balanced linear gain and
loss applied to the two cores, and cubic-quintic (CQ) nonlinearity acting in
each one. The 2D and 1D models may be realized in dual-core optical waveguides,
in the spatiotemporal and spatial domains, respectively. Stationary solutions
for $\mathcal{PT}$-symmetric solitons in these systems reduce to their
counterparts in the usual coupler. The most essential problem is the stability
of the solitons, which become unstable against symmetry breaking with the
increase of the energy (norm), and retrieve the stability at still larger
energies. The boundary value of the intercore-coupling constant, above which
the solitons are completely stable, is found by means of an analytical
approximation, based on the CW (zero-dimensional) counterpart of the system.
The approximation demonstrates good agreement with numerical findings for the
1D and 2D solitons. Numerical results for the stability limits of the 2D
solitons are obtained by means of the computation of eigenvalues for small
perturbations, and verified in direct simulations. Although large parts of the
solitons families are unstable, the instability is quite weak. Collisions
between 2D solitons in the $\mathcal{PT}$-symmetric coupler are studied by
means of simulations. Outcomes of the collisions are inelastic but not
destructive, as they do not break the $\mathcal{PT}$ symmetry.

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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: math-ph