365 research outputs found
PT-symmetric lattices with spatially extended gain/loss are generically unstable
We illustrate, through a series of prototypical examples, that linear
parity-time (PT) symmetric lattices with extended gain/loss profiles are
generically unstable, for any non-zero value of the gain/loss coefficient. Our
examples include a parabolic real potential with a linear imaginary part and
the cases of no real and constant or linear imaginary potentials. On the other
hand, this instability can be avoided and the spectrum can be real for
localized or compact PT-symmetric potentials. The linear lattices are analyzed
through discrete Fourier transform techniques complemented by numerical
computations.Comment: 6 pages, 4 figure
Beating dark-dark solitons and Zitterbewegung in spin-orbit coupled Bose-Einstein condensates
We present families of beating dark-dark solitons in spin-orbit (SO) coupled
Bose-Einstein condensates. These families consist of solitons residing
simultaneously in the two bands of the energy spectrum. The soliton components
are characterized by two different spatial and temporal scales, which are
identified by a multiscale expansion method. The solitons are "beating" ones,
as they perform density oscillations with a characteristic frequency, relevant
to Zitterbewegung (ZB). We find that spin oscillations may occur, depending on
the parity of each soliton branch, which consequently lead to ZB oscillations
of the beating dark solitons. Analytical results are corroborated by numerical
simulations, illustrating the robustness of the solitons.Comment: 6 pages, 3 figure
Crossover dark soliton dynamics in ultracold one-dimensional Bose gases
Ultracold confined one-dimensional atomic gases are predicted to support dark
soliton solutions arising from a nonlinear Schr\"{o}dinger equation of suitable
nonlinearity. In weakly-interacting (high density) gases, the nonlinearity is
cubic, whereas an approximate model for describing the behaviour of strongly -
interacting (low density) gases is one characterized by a quintic nonlinearity.
We use an approximate analytical expression for the form of the nonlinearity in
the intermediate regimes to show that, near the crossover between the two
different regimes, the soliton is predicted and numerically confirmed to
oscillate at a frequency of , where is the harmonic
trap frequency.Comment: To appear in Phys. Lett.
Matter-wave solitons of collisionally inhomogeneous condensates
We investigate the dynamics of matter-wave solitons in the presence of a
spatially varying atomic scattering length and nonlinearity. The dynamics of
bright and dark solitary waves is studied using the corresponding
Gross-Pitaevskii equation. The numerical results are shown to be in very good
agreement with the predictions of the effective equations of motion derived by
adiabatic perturbation theory. The spatially dependent nonlinearity leads to a
gravitational potential that allows to influence the motion of both fundamental
as well as higher order solitons.Comment: 19 pages, 4 figure
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
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