Blow-up solitons at the nonlinear stage of the two-stream instability in quantum plasmas

The nonlinear evolution of the quantum two-stream instability in a plasma with counter-streaming electron beams is studied. It is shown that in the long-wave limit the nonlinear stage of the instability can be described by the elliptic nonlinear string equation. We present two types of the nonlinear solutions. The first one is an unstable nonlinear mode that is continuously related with the growing linear solution and the second one is a pulsating soliton. We show that both of these solutions blow up in a finite time.Comment: https://iopscience.iop.org/article/10.1209/0295-5075/130/3000

NN-soliton solutions of the Fokas-Lenells equation for the plasma ion-cyclotron waves: Inverse scattering transform approach

We present a simple and constructive method to find $N$-soliton solutions of the equation suggested by Davydova and Lashkin to describe the dynamics of nonlinear ion-cyclotron waves in a plasma and subsequently known (in a more general form and as applied to nonlinear optics) as the Fokas-Lenells equation. Using the classical inverse scattering transform approach, we find bright $N$-soliton solutions, rational $N$-soliton solutions, and $N$-soliton solutions in the form of a mixture of exponential and rational functions. Explicit breather solutions are presented as examples. Unlike purely algebraic constructions of the Hirota or Darboux type, we also give a general expression for arbitrary initial data decaying at infinity, which contains the contribution of the continuous spectrum (radiation).Comment: arXiv admin note: text overlap with arXiv:2103.1009

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.

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

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

Excitation of zonal flow by the modulational instability in electron temperature gradient driven turbulence

The generation of large-scale zonal flows by small-scale electrostatic drift waves in electron temperature gradient(ETG) driven turbulence model is considered. The generation mechanism is based on the modulational instability of a finite amplitude monochromatic drift wave. The threshold and growth rate of the instability as well as the optimal spatial scale of zonal flow are obtained.Comment: 10 pages, 3 figure

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

Spinor-Induced Instability of Kinks, Holes and Quantum Droplets

We address the existence and stability of one-dimensional (1D) holes and kinks and two-dimensional (2D) vortex-holes nested in extended binary Bose mixtures, which emerge in the presence of Lee-Huang-Yang (LHY) quantum corrections to the mean-field energy, along with self-bound quantum droplets. We consider both the symmetric system with equal intra-species scattering lengths and atomic masses, modeled by a single (scalar) LHY-corrected Gross-Pitaevskii equation (GPE), and the general asymmetric case with different intra-species scattering lengths, described by two coupled (spinor) GPEs. We found that in the symmetric setting, 1D and 2D holes can exist in a stable form within a range of chemical potentials that overlaps with that of self-bound quantum droplets, but that extends far beyond it. In this case, holes are found to be stable in 1D and they transform into pairs of stable out-of-phase kinks at the critical chemical potential at which localized droplets turn into flat-top states, thereby revealing the connection between localized and extended nonlinear states. In contrast, spinor nature of the asymmetric systems may lead to instability of 1D holes, which tend to break into two gray states moving in the opposite directions. Such instability arises due to spinor nature of the system and it affects only holes nested in extended modulationally-stable backgrounds, while localized quantum droplet families remain completely stable, even in the asymmetric case, while 1D holes remain stable only close to the point where they transform into pairs of kinks. We also found that symmetric systems allow fully stable 2D vortex-carrying single-charge states at moderate amplitudes, while unconventional instabilities appear also at high amplitudes. Symmetry also strongly inhibits instabilities for double-charge vortex-holes, which thus exhibit unexpectedly robust evolutions at low amplitudes.Comment: 9 pages, 7 figures, to appear in New Journal of Physic