Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transitions between symmetric and asymmetric solitons in dual-core
  systems with cubic-quintic nonlinearity   It is well known that a symmetric soliton in coupled nonlinear Schroedinger
(NLS) equations with the cubic nonlinearity loses its stability with the
increase of its energy, featuring a transition into an asymmetric soliton via a
subcritical bifurcation. A similar phenomenon was found in a dual-core system
with quadratic nonlinearity, and in linearly coupled fiber Bragg gratings, with
a difference that the symmetry-breaking bifurcation is supercritical in those
cases. We aim to study transitions between symmetric and asymmetric solitons in
dual-core systems with saturable nonlinearity. We demonstrate that a basic
model of this type, viz., a pair of linearly coupled NLS equations with the
intra-core cubic-quintic (CQ) nonlinearity, features a bifurcation loop: a
symmetric soliton loses its stability via a supercritical bifurcation, which is
followed, at a larger value of the energy, by a reverse bifurcation that
restores the stability of the symmetric soliton. If the linear-coupling
constant is small enough, the second bifurcation is subcritical, and there is a
broad interval of energies in which the system is bistable, with coexisting
stable symmetric and asymmetric solitons. At larger values of the coupling
constant, the reverse bifurcation is supercritical, and the bifurcation loop
disappears if the linear coupling is very strong. Collisions between moving
solitons are studied too. Symmetric solitons always collide elastically, while
collisions between asymmetric solitons turns them into breathers, that
subsequently undergo dynamical symmetrization.

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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-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
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The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio