52 research outputs found
Anisotropic solitons in dipolar Bose-Einstein Condensates
Starting with a Gaussian variational ansatz, we predict anisotropic bright
solitons in quasi-2D Bose-Einstein condensates consisting of atoms with dipole
moments polarized \emph{perpendicular} to the confinement direction. Unlike
isotropic solitons predicted for the moments aligned with the confinement axis
[Phys. Rev. Lett. \textbf{95}, 200404 (2005)], no sign reversal of the
dipole-dipole interaction is necessary to support the solitons. Direct 3D
simulations confirm their stability.Comment: 5 pages, 4 figure
Interaction of pulses in nonlinear Schroedinger model
The interaction of two rectangular pulses in nonlinear Schroedinger model is
studied by solving the appropriate Zakharov-Shabat system. It is shown that two
real pulses may result in appearance of moving solitons. Different limiting
cases, such as a single pulse with a phase jump, a single chirped pulse,
in-phase and out-of-phase pulses, and pulses with frequency separation, are
analyzed. The thresholds of creation of new solitons and multi-soliton states
are found.Comment: 9 pages, 7 figures. Accepted to Phys. Rev. E, 200
Nonlinear coupled Alfv\'{e}n and gravitational waves
In this paper we consider nonlinear interaction between gravitational and
electromagnetic waves in a strongly magnetized plasma. More specifically, we
investigate the propagation of gravitational waves with the direction of
propagation perpendicular to a background magnetic field, and the coupling to
compressional Alfv\'{e}n waves. The gravitational waves are considered in the
high frequency limit and the plasma is modelled by a multifluid description. We
make a self-consistent, weakly nonlinear analysis of the Einstein-Maxwell
system and derive a wave equation for the coupled gravitational and
electromagnetic wave modes. A WKB-approximation is then applied and as a result
we obtain the nonlinear Schr\"{o}dinger equation for the slowly varying wave
amplitudes. The analysis is extended to 3D wave pulses, and we discuss the
applications to radiation generated from pulsar binary mergers. It turns out
that the electromagnetic radiation from a binary merger should experience a
focusing effect, that in principle could be detected.Comment: 20 pages, revtex4, accepted in PR
Stability and collective excitations of a two-component Bose-condensed gas: a moment approach
The dynamics of a two-component dilute Bose gas of atoms at zero temperature
is described in the mean field approximation by a two-component
Gross-Pitaevskii Equation. We solve this equation assuming a Gaussian shape for
the wavefunction, where the free parameters of the trial wavefunction are
determined using a moment method. We derive equilibrium states and the phase
diagrams for the stability for positive and negative s-wave scattering lengths,
and obtain the low energy excitation frequencies corresponding to the
collective motion of the two Bose condensates.Comment: 7 pages, 6 figure
Soliton formation from a pulse passing the zero-dispersion point in a nonlinear Schr\"odinger equation
We consider in detail the self-trapping of a soliton from a wave pulse that
passes from a defocussing region into a focussing one in a spatially
inhomogeneous nonlinear waveguide, described by a nonlinear Schrodinger
equation in which the dispersion coefficient changes its sign from normal to
anomalous. The model has direct applications to dispersion-decreasing nonlinear
optical fibers, and to natural waveguides for internal waves in the ocean. It
is found that, depending on the (conserved) energy and (nonconserved) mass of
the initial pulse, four qualitatively different outcomes of the pulse
transformation are possible: decay into radiation; self-trapping into a single
soliton; formation of a breather; and formation of a pair of counterpropagating
solitons. A corresponding chart is drawn on a parametric plane, which
demonstrates some unexpected features. In particular, it is found that any kind
of soliton(s) (including the breather and counterpropagating pair) eventually
decays into pure radiation with the increase of the energy, the initial mass
being kept constant. It is also noteworthy that a virtually direct transition
from a single soliton into a pair of symmetric counterpropagating ones seems
possible. An explanation for these features is proposed. In two cases when
analytical approximations apply, viz., a simple perturbation theory for broad
initial pulses, or the variational approximation for narrow ones, comparison
with the direct simulations shows reasonable agreement.Comment: 18 pages, 10 figures, 1 table. Phys. Rev. E, in pres
On the Properties of Two Pulses Propagating Simultaneously in Different Dispersion Regimes in a Nonlinear Planar Waveguide
Properties of two pulses propagating simultaneously in different dispersion
regimes, anomalous and normal, in a Kerr-type planar waveguide are studied in
the framework of the nonlinear Schroedinger equation. Catastrophic
self-focusing and spatio-temporal splitting of the pulses is investigated. For
the limiting case when the dispersive term of the pulse propagating in the
normal dispersion regime can be neglected an indication of a possibility of a
stable self-trapped propagation of both pulses is obtained.Comment: 18 pages (including 15 eps figures
Stability of trapped Bose-Einstein condensates
In three-dimensional trapped Bose-Einstein condensate (BEC), described by the
time-dependent Gross-Pitaevskii-Ginzburg equation, we study the effect of
initial conditions on stability using a Gaussian variational approach and exact
numerical simulations. We also discuss the validity of the criterion for
stability suggested by Vakhitov and Kolokolov. The maximum initial chirp
(initial focusing defocusing of cloud) that can lead a stable condensate to
collapse even before the number of atoms reaches its critical limit is obtained
for several specific cases. When we consider two- and three-body nonlinear
terms, with negative cubic and positive quintic terms, we have the conditions
for the existence of two phases in the condensate. In this case, the magnitude
of the oscillations between the two phases are studied considering sufficient
large initial chirps. The occurrence of collapse in a BEC with repulsive
two-body interaction is also shown to be possible.Comment: 15 pages, 11 figure
Ultrashort filaments of light in weakly-ionized, optically-transparent media
Modern laser sources nowadays deliver ultrashort light pulses reaching few
cycles in duration, high energies beyond the Joule level and peak powers
exceeding several terawatt (TW). When such pulses propagate through
optically-transparent media, they first self-focus in space and grow in
intensity, until they generate a tenuous plasma by photo-ionization. For free
electron densities and beam intensities below their breakdown limits, these
pulses evolve as self-guided objects, resulting from successive equilibria
between the Kerr focusing process, the chromatic dispersion of the medium, and
the defocusing action of the electron plasma. Discovered one decade ago, this
self-channeling mechanism reveals a new physics, widely extending the frontiers
of nonlinear optics. Implications include long-distance propagation of TW beams
in the atmosphere, supercontinuum emission, pulse shortening as well as
high-order harmonic generation. This review presents the landmarks of the
10-odd-year progress in this field. Particular emphasis is laid to the
theoretical modeling of the propagation equations, whose physical ingredients
are discussed from numerical simulations. Differences between femtosecond
pulses propagating in gaseous or condensed materials are underlined. Attention
is also paid to the multifilamentation instability of broad, powerful beams,
breaking up the energy distribution into small-scale cells along the optical
path. The robustness of the resulting filaments in adverse weathers, their
large conical emission exploited for multipollutant remote sensing, nonlinear
spectroscopy, and the possibility to guide electric discharges in air are
finally addressed on the basis of experimental results.Comment: 50 pages, 38 figure
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