92 research outputs found
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
Propagation studies for the construction of atomic macro-coherence in dense media as a tool to investigate neutrino physics
In this manuscript we review the possibility of inducing large coherence in a
macroscopic dense target by using adiabatic techniques. For this purpose we
investigate the degradation of the laser pulse through propagation, which was
also related to the size of the prepared medium. Our results show that,
although adiabatic techniques offer the best alternative in terms of stability
against experimental parameters, for very dense media it is necessary to
engineer laser-matter interaction in order to minimize laser field degradation.
This work has been triggered by the proposal of a new technique, namely
Radiative Emission of Neutrino Pairs (RENP), capable of investigating neutrino
physics through quantum optics concepts which require the preparation of a
macrocoherent state.Comment: 10 pages, 10 figure
Impulse-induced localized nonlinear modes in an electrical lattice
Intrinsic localized modes, also called discrete breathers, can exist under
certain conditions in one-dimensional nonlinear electrical lattices driven by
external harmonic excitations. In this work, we have studied experimentally the
efectiveness of generic periodic excitations of variable waveform at generating
discrete breathers in such lattices. We have found that this generation
phenomenon is optimally controlled by the impulse transmitted by the external
excitation (time integral over two consecutive zerosComment: 5 pages, 8 figure
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
Stabilization of the Peregrine soliton and Kuznetsov-Ma breathers by means of nonlinearity and dispersion management
We demonstrate a possibility to make rogue waves (RWs) in the form of the
Peregrine soliton (PS) and Kuznetsov-Ma breathers (KMBs) effectively stable
objects, with the help of properly defined dispersion or nonlinearity
management applied to the continuous-wave (CW) background supporting the RWs.
In particular, it is found that either management scheme, if applied along the
longitudinal coordinate, making the underlying nonlinear Schr\"odinger equation
(NLSE) selfdefocusing in the course of disappearance of the PS, indeed
stabilizes the global solution with respect to the modulational instability of
the background. In the process, additional excitations are generated, namely,
dispersive shock waves and, in some cases, also a pair of slowly separating
dark solitons. Further, the nonlinearity-management format, which makes the
NLSE defocusing outside of a finite domain in the transverse direction, enables
the stabilization of the KMBs, in the form of confined oscillating states. On
the other hand, a nonlinearity-management format applied periodically along the
propagation direction, creates expanding patterns featuring multiplication of
KMBs through their cascading fission.Comment: Physics Letters A, on pres
Speed-of-light pulses in a nonlinear Weyl equation
We introduce a prototypical nonlinear Weyl equation, motivated by recent
developments in massless Dirac fermions, topological semimetals and photonics.
We study the dynamics of its pulse solutions and find that a localized one-hump
initial condition splits into a localized two-hump pulse, while an associated
phase structure emerges in suitable components of the spinor field. For times
larger than a transient time this pulse moves with the speed of light (or
Fermi velocity in Weyl semimetals), effectively featuring linear wave dynamics
and maintaining its shape (both in two and three dimensions). We show that for
the considered nonlinearity, this pulse represents an exact solution of the
nonlinear Weyl (NLW) equation. Finally, we comment on the generalization of the
results to a broader class of nonlinearities and on their emerging potential
for observation in different areas of application.Comment: 7 pages, 6 figure
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
Collective Coordinates Theory for Discrete Soliton Ratchets in the sine-Gordon Model
A collective coordinate theory is develop for soliton ratchets in the damped
discrete sine-Gordon model driven by a biharmonic force. An ansatz with two
collective coordinates, namely the center and the width of the soliton, is
assumed as an approximated solution of the discrete non-linear equation. The
evolution of these two collective coordinates, obtained by means of the
Generalized Travelling Wave Method, explains the mechanism underlying the
soliton ratchet and captures qualitatively all the main features of this
phenomenon. The theory accounts for the existence of a non-zero depinning
threshold, the non-sinusoidal behaviour of the average velocity as a function
of the difference phase between the harmonics of the driver, the non-monotonic
dependence of the average velocity on the damping and the existence of
non-transporting regimes beyond the depinning threshold. In particular it
provides a good description of the intriguing and complex pattern of subspaces
corresponding to different dynamical regimes in parameter space
Reaction-diffusion spatial modeling of COVID-19: Greece and Andalusia as case examples
We examine the spatial modeling of the outbreak of COVID-19 in two regions:
the autonomous community of Andalusia in Spain and the mainland of Greece. We
start with a 0D compartmental epidemiological model consisting of Susceptible,
Exposed, Asymptomatic, (symptomatically) Infected, Hospitalized, Recovered, and
deceased populations. We emphasize the importance of the viral latent period
and the key role of an asymptomatic population. We optimize model parameters
for both regions by comparing predictions to the cumulative number of infected
and total number of deaths via minimizing the norm of the difference
between predictions and observed data. We consider the sensitivity of model
predictions on reasonable variations of model parameters and initial
conditions, addressing issues of parameter identifiability. We model both
pre-quarantine and post-quarantine evolution of the epidemic by a
time-dependent change of the viral transmission rates that arises in response
to containment measures. Subsequently, a spatially distributed version of the
0D model in the form of reaction-diffusion equations is developed. We consider
that, after an initial localized seeding of the infection, its spread is
governed by the diffusion (and 0D model "reactions") of the asymptomatic and
symptomatically infected populations, which decrease with the imposed
restrictive measures. We inserted the maps of the two regions, and we imported
population-density data into COMSOL, which was subsequently used to solve
numerically the model PDEs. Upon discussing how to adapt the 0D model to this
spatial setting, we show that these models bear significant potential towards
capturing both the well-mixed, 0D description and the spatial expansion of the
pandemic in the two regions. Veins of potential refinement of the model
assumptions towards future work are also explored.Comment: 28 pages, 16 figures and 2 movie
- …