9,194 research outputs found
Josephson tunneling of dark solitons in a double-well potential
We study the dynamics of matter waves in an effectively one-dimensional
Bose-Einstein condensate in a double well potential. We consider in particular
the case when one of the double wells confines excited states. Similarly to the
known ground state oscillations, the states can tunnel between the wells
experiencing the physics known for electrons in a Josephson junction, or be
self-trapped. As the existence of dark solitons in a harmonic trap are
continuations of such non-ground state excitations, one can view the
Josephson-like oscillations as tunnelings of dark solitons. Numerical existence
and stability analysis based on the full equation is performed, where it is
shown that such tunneling can be stable. Through a numerical path following
method, unstable tunneling is also obtained in different parameter regions. A
coupled-mode system is derived and compared to the numerical observations.
Regions of (in)stability of Josephson tunneling are discussed and highlighted.
Finally, we outline an experimental scheme designed to explore such dark
soliton dynamics in the laboratory.Comment: submitte
PT-symmetric sine-Gordon breathers
In this work, we explore a prototypical example of a genuine continuum
breather (i.e., not a standing wave) and the conditions under which it can
persist in a -symmetric medium. As our model of interest, we
will explore the sine-Gordon equation in the presence of a -
symmetric perturbation. Our main finding is that the breather of the
sine-Gordon model will only persist at the interface between gain and loss that
-symmetry imposes but will not be preserved if centered at the
lossy or at the gain side. The latter dynamics is found to be interesting in
its own right giving rise to kink-antikink pairs on the gain side and complete
decay of the breather on the lossy side. Lastly, the stability of the breathers
centered at the interface is studied. As may be anticipated on the basis of
their "delicate" existence properties such breathers are found to be
destabilized through a Hopf bifurcation in the corresponding Floquet analysis
Coupled backward- and forward-propagating solitons in a composite right/left-handed transmission line
We study the coupling between backward- and forward-propagating wave modes,
with the same group velocity, in a composite right/left-handed nonlinear
transmission line. Using an asymptotic multiscale expansion technique, we
derive a system of two coupled nonlinear Schr{\"o}dinger equations governing
the evolution of the envelopes of these modes. We show that this system
supports a variety of backward- and forward propagating vector solitons, of the
bright-bright, bright-dark and dark-bright type. Performing systematic
numerical simulations in the framework of the original lattice that models the
transmission line, we study the propagation properties of the derived vector
soliton solutions. We show that all types of the predicted solitons exist, but
differ on their robustness: only bright-bright solitons propagate undistorted
for long times, while the other types are less robust, featuring shorter
lifetimes. In all cases, our analytical predictions are in a very good
agreement with the results of the simulations, at least up to times of the
order of the solitons' lifetimes
A Unifying Perspective: Solitary Traveling Waves As Discrete Breathers And Energy Criteria For Their Stability
In this work, we provide two complementary perspectives for the (spectral)
stability of solitary traveling waves in Hamiltonian nonlinear dynamical
lattices, of which the Fermi-Pasta-Ulam and the Toda lattice are prototypical
examples. One is as an eigenvalue problem for a stationary solution in a
co-traveling frame, while the other is as a periodic orbit modulo shifts. We
connect the eigenvalues of the former with the Floquet multipliers of the
latter and based on this formulation derive an energy-based spectral stability
criterion. It states that a sufficient (but not necessary) condition for a
change in the wave stability occurs when the functional dependence of the
energy (Hamiltonian) of the model on the wave velocity changes its
monotonicity. Moreover, near the critical velocity where the change of
stability occurs, we provide explicit leading-order computation of the unstable
eigenvalues, based on the second derivative of the Hamiltonian
evaluated at the critical velocity . We corroborate this conclusion with a
series of analytically and numerically tractable examples and discuss its
parallels with a recent energy-based criterion for the stability of discrete
breathers
Nucleation of breathers via stochastic resonance in nonlinear lattices
By applying a staggered driving force in a prototypical discrete model with a
quartic nonlinearity, we demonstrate the spontaneous formation and destruction
of discrete breathers with a selected frequency due to thermal fluctuations.
The phenomenon exhibits the striking features of stochastic resonance (SR): a
nonmonotonic behavior as noise is increased and breather generation under
subthreshold conditions. The corresponding peak is associated with a matching
between the external driving frequency and the breather frequency at the
average energy given by ambient temperature.Comment: Added references, figure 5 modified to include new dat
Solitary waves in a two-dimensional nonlinear Dirac equation: from discrete to continuum
In the present work, we explore a nonlinear Dirac equation motivated as the
continuum limit of a binary waveguide array model. We approach the problem both
from a near-continuum perspective as well as from a highly discrete one.
Starting from the former, we see that the continuum Dirac solitons can be
continued for all values of the discretization (coupling) parameter, down to
the uncoupled (so-called anti-continuum) limit where they result in a 9-site
configuration. We also consider configurations with 1- or 2-sites at the
anti-continuum limit and continue them to large couplings, finding that they
also persist. For all the obtained solutions, we examine not only the
existence, but also the spectral stability through a linearization analysis and
finally consider prototypical examples of the dynamics for a selected number of
cases for which the solutions are found to be unstable
Breather trapping and breather transmission in a DNA model with an interface
We study the dynamics of moving discrete breathers in an interfaced piecewise
DNA molecule.
This is a DNA chain in which all the base pairs are identical and there
exists an interface such that the base pairs dipole moments at each side are
oriented in opposite directions.
The Hamiltonian of the Peyrard--Bishop model is augmented with a term that
includes the dipole--dipole coupling between base pairs. Numerical simulations
show the existence of two dynamical regimes. If the translational kinetic
energy of a moving breather launched towards the interface is below a critical
value, it is trapped in a region around the interface collecting vibrational
energy. For an energy larger than the critical value, the breather is
transmitted and continues travelling along the double strand with lower
velocity. Reflection phenomena never occur.
The same study has been carried out when a single dipole is oriented in
opposite direction to the other ones.
When moving breathers collide with the single inverted dipole, the same
effects appear. These results emphasize the importance of this simple type of
local inhomogeneity as it creates a mechanism for the trapping of energy.
Finally, the simulations show that, under favorable conditions, several
launched moving breathers can be trapped successively at the interface region
producing an accumulation of vibrational energy. Moreover, an additional
colliding moving breather can produce a saturation of energy and a moving
breather with all the accumulated energy is transmitted to the chain.Comment: 15 pages, 11 figure
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