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 $k$ and frequency $\omega$, the motion of the SPs being possible at velocities $\pm \omega /k$, 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 $0< k < 1/\sqrt{2}$ $(1/\sqrt{2}<k<1)$. 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