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