257 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
Special solutions to a compact equation for deep-water gravity waves
Recently, Dyachenko & Zakharov (2011) have derived a compact form of the well
known Zakharov integro-differential equation for the third order Hamiltonian
dynamics of a potential flow of an incompressible, infinitely deep fluid with a
free surface. Special traveling wave solutions of this compact equation are
numerically constructed using the Petviashvili method. Their stability
properties are also investigated. Further, unstable traveling waves with
wedge-type singularities, viz. peakons, are numerically discovered. To gain
insights into the properties of singular traveling waves, we consider the
academic case of a perturbed version of the compact equation, for which
analytical peakons with exponential shape are derived. Finally, by means of an
accurate Fourier-type spectral scheme it is found that smooth solitary waves
appear to collide elastically, suggesting the integrability of the Zakharov
equation.Comment: 17 pages, 14 figures, 41 references. Other author's papers can be
downloaded at http://www.lama.univ-savoie.fr/~dutykh
Rogue waves in the atmosphere
The appearance of rogue waves is well known in oceanographics, optics, and
cold matter systems. Here we show a possibility for the existence of
atmospheric rogue waves.Comment: 2 pages, 1 figur
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
Amplitude modulated drift wave packets in a nonuniform magnetoplasma
We consider the amplitude modulation of low-frequency, long wavelength
electrostatic drift wave packets in a nonuniform magnetoplasma with the effects
of equilibrium density, electron temperature and magnetic field
inhomogeneities. The dynamics of the modulated drift wave packet is governed by
a nonlinear Schr\"odinger equation. The latter is used to study the
modulational instability of a Stoke's wave train to a small longitudinal
perturbation. It is shown that the drift wave packet is stable (unstable)
against the modulation when the drift wave number lies in
. Thus, the modulated drift wave packet can propagate in the
form of bright and dark envelope solitons or as a drift wave rogon.Comment: 4 pages, 4figure
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
Magnetosonic solitons in a dusty plasma slab
The existence of magnetosonic solitons in dusty plasmas is investigated. The
nonlinear magnetohydrodynamic equations for a warm dusty magnetoplasma are thus
derived. A solution of the nonlinear equations is presented. It is shown that,
due to the presence of dust, static structures are allowed. This is in sharp
contrast to the formation of the so called shocklets in usual magnetoplasmas. A
comparatively small number of dust particles can thus drastically alter the
behavior of the nonlinear structures in magnetized plasmas.Comment: 7 pages, 6 figure
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