5,579 research outputs found
Cooperative jump motions of jammed particles in a one-dimensional periodic potential
Cooperative jump motions are studied for mutually interacting particles in a
one-dimensional periodic potential. The diffusion constant for the cooperative
motion in systems including a small number of particles is numerically
calculated and it is compared with theoretical estimates. We find that the size
distribution of the cooperative jump motions obeys an exponential law in a
large system.Comment: 5 pages, 4 figure
Stable localized pulses and zigzag stripes in a two-dimensional diffractive-diffusive Ginzburg-Landau equation
We introduce a model of a two-dimensional (2D) optical waveguide with Kerr
nonlinearity, linear and quintic losses, cubic gain, and temporal-domain
filtering. In the general case, temporal dispersion is also included, although
it is not necessary. The model provides for description of a nonlinear planar
waveguide incorporated into a closed optical cavity. It takes the form of a 2D
cubic-quintic Ginzburg-Landau equation with an anisotropy of a novel type: the
equation is diffractive in one direction, and diffusive in the other. By means
of systematic simulations, we demonstrate that the model gives rise to
\emph{stable} fully localized 2D pulses, which are spatiotemporal ``light
bullets'', existing due to the simultaneous balances between diffraction,
dispersion, and Kerr nonlinearity, and between linear and quintic losses and
cubic gain. A stability region of the 2D pulses is identified in the system's
parameter space. Besides that, we also find that the model generates 1D
patterns in the form of simple localized stripes, which may be stable, or may
exhibit an instability transforming them into oblique stripes with zigzags. The
straight and oblique stripes may stably coexist with the 2D pulse, but not with
each other.Comment: 16pages, 9figure
Solitons in combined linear and nonlinear lattice potentials
We study ordinary solitons and gap solitons (GSs) in the effectively
one-dimensional Gross-Pitaevskii equation, with a combination of linear and
nonlinear lattice potentials. The main points of the analysis are effects of
the (in)commensurability between the lattices, the development of analytical
methods, viz., the variational approximation (VA) for narrow ordinary solitons,
and various forms of the averaging method for broad solitons of both types, and
also the study of mobility of the solitons. Under the direct commensurability
(equal periods of the lattices, the family of ordinary solitons is similar to
its counterpart in the free space. The situation is different in the case of
the subharmonic commensurability, with L_{lin}=(1/2)L_{nonlin}, or
incommensurability. In those cases, there is an existence threshold for the
solitons, and the scaling relation between their amplitude and width is
different from that in the free space. GS families demonstrate a bistability,
unless the direct commensurability takes place. Specific scaling relations are
found for them too. Ordinary solitons can be readily set in motion by kicking.
GSs are mobile too, featuring inelastic collisions. The analytical
approximations are shown to be quite accurate, predicting correct scaling
relations for the soliton families in different cases. The stability of the
ordinary solitons is fully determined by the VK (Vakhitov-Kolokolov) criterion,
while the stability of GS families follows an inverted ("anti-VK") criterion,
which is explained by means of the averaging approximation.Comment: 9 pages, 6 figure
Instability of synchronized motion in nonlocally coupled neural oscillators
We study nonlocally coupled Hodgkin-Huxley equations with excitatory and
inhibitory synaptic coupling. We investigate the linear stability of the
synchronized solution, and find numerically various nonuniform oscillatory
states such as chimera states, wavy states, clustering states, and
spatiotemporal chaos as a result of the instability.Comment: 8 pages, 9 figure
Localized matter-waves patterns with attractive interaction in rotating potentials
We consider a two-dimensional (2D) model of a rotating attractive
Bose-Einstein condensate (BEC), trapped in an external potential. First, an
harmonic potential with the critical strength is considered, which generates
quasi-solitons at the lowest Landau level (LLL). We describe a family of the
LLL quasi-solitons using both numerical method and a variational approximation
(VA), which are in good agreement with each other. We demonstrate that kicking
the LLL mode or applying a ramp potential sets it in the Larmor (cyclotron)
motion, that can also be accurately modeled by the VA.Comment: 13 pages, 11 figure
Power-dependent shaping of vortex solitons in optical lattices with spatially modulated nonlinear refractive index
We address vortex solitons supported by optical lattices featuring modulation
of both the linear and nonlinear refractive indices. We find that when the
modulation is out-of-phase the competition between both effects results in
remarkable shape transformations of the solitons which profoundly affect their
properties and stability. Nonlinear refractive index modulation is found to
impose restrictions on the maximal power of off-site solitons, which are shown
to be stable only below a maximum nonlinearity modulation depth.Comment: 11 pages, 3 figures, to appear in Optics Letter
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