127 research outputs found
Two-dimensional multisolitons and azimuthons in Bose-Einstein condensates with attraction
We present spatially localized nonrotating and rotating (azimuthon)
multisolitons in the two-dimensional (2D) ("pancake-shaped configuration")
Bose-Einstein condensate (BEC) with attractive interaction. By means of a
linear stability analysis, we investigate the stability of these structures and
show that rotating dipole solitons are stable provided that the number of atoms
is small enough. The results were confirmed by direct numerical simulations of
the 2D Gross-Pitaevskii equation.Comment: 4 pages, 4 figure
Two-dimensional nonlocal vortices, multipole solitons and azimuthons in dipolar Bose-Einstein condensates
We have performed numerical analysis of the two-dimensional (2D) soliton
solutions in Bose-Einstein condensates with nonlocal dipole-dipole
interactions. For the modified 2D Gross-Pitaevski equation with nonlocal and
attractive local terms, we have found numerically different types of nonlinear
localized structures such as fundamental solitons, radially symmetric vortices,
nonrotating multisolitons (dipoles and quadrupoles), and rotating multisolitons
(azimuthons). By direct numerical simulations we show that these structures can
be made stable.Comment: 6 pages, 6 figures, submitted to Phys. Rev.
Moving and colliding pulses in the subcritical Ginzburg-Landau model with a standing-wave drive
We show the existence of steadily moving solitary pulses (SPs) in the complex
Ginzburg-Landau (CGL) equation, which includes the cubic-quintic (CQ)
nonlinearity and a conservative linear driving term, whose amplitude is a
standing wave with wavenumber and frequency , the motion of the
SPs being possible at velocities , which provide locking to the
drive. A realization of the model may be provided by traveling-wave convection
in a narrow channel with a standing wave excited in its bottom (or on the
surface). An analytical approximation is developed, based on an effective
equation of motion for the SP coordinate. Direct simulations demonstrate that
the effective equation accurately predicts characteristics of the driven motion
of pulses, such as a threshold value of the drive's amplitude. Collisions
between two solitons traveling in opposite directions are studied by means of
direct simulations, which reveal that they restore their original shapes and
velocity after the collision.Comment: 7 pages, 5 eps figure
Two-dimensional ring-like vortex and multisoliton nonlinear structures at the upper-hybrid resonance
Two-dimensional (2D) equations describing the nonlinear interaction between
upper-hybrid and dispersive magnetosonic waves are presented. Nonlocal
nonlinearity in the equations results in the possibility of existence of stable
2D nonlinear structures. A rigorous proof of the absence of collapse in the
model is given. We have found numerically different types of nonlinear
localized structures such as fundamental solitons, radially symmetric vortices,
nonrotating multisolitons (two-hump solitons, dipoles and quadrupoles), and
rotating multisolitons (azimuthons). By direct numerical simulations we show
that 2D fundamental solitons with negative hamiltonian are stable.Comment: 8 pages, 6 figures, submitted to Phys. Plasma
Traveling waves and Compactons in Phase Oscillator Lattices
We study waves in a chain of dispersively coupled phase oscillators. Two
approaches -- a quasi-continuous approximation and an iterative numerical
solution of the lattice equation -- allow us to characterize different types of
traveling waves: compactons, kovatons, solitary waves with exponential tails as
well as a novel type of semi-compact waves that are compact from one side.
Stability of these waves is studied using numerical simulations of the initial
value problem.Comment: 22 pages, 25 figure
The effect of sheared diamagnetic flow on turbulent structures generated by the Charney–Hasegawa–Mima equation
The generation of electrostatic drift wave turbulence is modelled by the Charney–Hasegawa–Mima equation. The equilibrium density gradient n0=n0(x) is chosen so that dn0 /dx is nonzero and spatially variable (i.e., v*e is sheared). It is shown that this sheared diamagnetic flow leads to localized turbulence which is concentrated at max(grad n0), with a large dv*e/dx inhibiting the spread of the turbulence in the x direction. Coherent structures form which propagate with the local v*e in the y direction. Movement in the x direction is accompanied by a change in their amplitudes. When the numerical code is initialized with a single wave, the plasma behaviour is dominated by the initial mode and its harmonics
Quasi-Two-Dimensional Dynamics of Plasmas and Fluids
In the lowest order of approximation quasi-twa-dimensional dynamics of planetary atmospheres and of plasmas in a magnetic field can be described by a common convective vortex equation, the Charney and Hasegawa-Mirna (CHM) equation. In contrast to the two-dimensional Navier-Stokes equation, the CHM equation admits "shielded vortex solutions" in a homogeneous limit and linear waves ("Rossby waves" in the planetary atmosphere and "drift waves" in plasmas) in the presence of inhomogeneity. Because of these properties, the nonlinear dynamics described by the CHM equation provide rich solutions which involve turbulent, coherent and wave behaviors. Bringing in non ideal effects such as resistivity makes the plasma equation significantly different from the atmospheric equation with such new effects as instability of the drift wave driven by the resistivity and density gradient. The model equation deviates from the CHM equation and becomes coupled with Maxwell equations. This article reviews the linear and nonlinear dynamics of the quasi-two-dimensional aspect of plasmas and planetary atmosphere starting from the introduction of the ideal model equation (CHM equation) and extending into the most recent progress in plasma turbulence.U. S. Department of Energy DE-FG05-80ET-53088Ministry of Education, Science and Culture of JapanFusion Research Cente
Compactons and Chaos in Strongly Nonlinear Lattices
We study localized traveling waves and chaotic states in strongly nonlinear
one-dimensional Hamiltonian lattices. We show that the solitary waves are
super-exponentially localized, and present an accurate numerical method
allowing to find them for an arbitrary nonlinearity index. Compactons evolve
from rather general initially localized perturbations and collide nearly
elastically, nevertheless on a long time scale for finite lattices an extensive
chaotic state is generally observed. Because of the system's scaling, these
dynamical properties are valid for any energy
Two-dimensional nonlinear vector states in Bose-Einstein condensates
Two-dimensional (2D) vector matter waves in the form of soliton-vortex and
vortex-vortex pairs are investigated for the case of attractive intracomponent
interaction in two-component Bose-Einstein condensates. Both attractive and
repulsive intercomponent interactions are considered. By means of a linear
stability analysis we show that soliton-vortex pairs can be stable in some
regions of parameters while vortex-vortex pairs turn out to be always unstable.
The results are confirmed by direct numerical simulations of the 2D coupled
Gross-Pitaevskii equations.Comment: 6 pages, 9 figure
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