斑图形成与孤子

We perform a computationl study of front speeds of G-equation models in time dependent cellular flows. The G-equations arise in premixed turbulent combustion, and are Hamilton-Jacobi type level set partial differential equations (PDEs). The…

We study the effects of noise on the dynamics of a system of coupled self-propelling particles in the case where the coupling is time-delayed, and the delays are discrete and randomly generated. Previous work has demonstrated that the…

We study modes trapped in a rotating ring with the local strength of the nonlinearity modulated as cos(2\theta), where \theta is the azimuthal angle. This modulation pattern may be of three different types: self-focusing (SF),…

We experimentally demonstrate the formation and stable propagation of various types of discrete temporal solitons in an optical fiber system. Pulses interacting with a time-periodic potential and defocusing nonlinearity are shown to form…

We consider the phenomenon of collapse in the critical Keller-Segel equation (KS) which models chemotactic aggregation of micro-organisms underlying many social activities, e.g. fruiting body development and biofilm formation. Also KS…

Plasmodium of \emph{Physarum polycephalum} is a single cell visible by unaided eye. On a non-nutrient substrate the plasmodium propagates as a traveling localization, as a compact wave-fragment of protoplasm. The plasmodium-localization…

A plasmodium of Physarum polycephalum is a very large cell visible by unaided eye. The plasmodium is capable for distributed sensing, parallel information processing, and decentralized optimization. It is an ideal substrate for future and…

We demonstrate an improved technique for implementing logic circuits in light-sensitive chemical excitable media. The technique makes use of the constant-speed propagation of waves along defined channels in an excitable medium based on the…

I propose that the labyrinthine patterns of the cortices of mammalian brains may be formed by a Turing instability of interacting axonal guidance species acting together with the mechanical strain imposed by the interconnecting axons.

We theoretically demonstrate the possibility to observe the macroscopic Zeno effect for nonlinear waveguides with a localized dissipation. We show the existence of stable stationary flows, which are balanced by the losses in the dissipative…

The propagation and controlled manipulation of strongly nonlinear, two-dimensional solitonic states in a thin, anisotropic ferromagnet are theoretically demonstrated. It has been recently proposed that spin-polarized currents in a…

Crystal growth has been widely studied for many years, and, since the pioneering work of Burton, Cabrera and Frank, spirals and target patterns on the crystal surface have been understood as forms of tangential crystal growth mediated by…

We look ahead from the frontiers of research on ice dynamics in its broadest sense; on the structures of ice, the patterns or morphologies it may assume, and the physical and chemical processes in which it is involved. We highlight open…

The spatiotemporal vortex lattices generated in high Fresnel number solid-state microchip lasers are studied in connection with Talbot phenomenon generic to spatially periodic electromagnetic fields. The spatial layout of light field is…

Exact expressions are obtained for a diversity of propagating patterns for a derivative nonlinear Schr\"odinger equation with a quintic nonlinearity. These patterns include bright pulses, fronts and dark solitons. The evolution of the wave…

Problems of interface growth have received much attention recently Such are, for example, the duffusion limited aggregation (DLA), random sequential adsorption (RSA), Laplacian growth or flame front propagation. We will mainly pay attention…

In this work we analyze PT-symmetric double-well potentials based on a two-mode picture. We reduce the problem into a PT-symmetric dimer and illustrate that the latter has effectively two fundamental bifurcations, a pitchfork…

In a previous work[1] exact stable oblique soliton solutions were revealed in two dimensional nonlinear Schroedinger flow. In this work we show that single soliton solution can be expressed within the Hirota bilinear formalism. An attempt…

Light-sensitive modification (ruthenium catalysed) of the Belousov-Zhabotinsky medium exhibits various regimes of excitability depending on the levels of illumination. For certain values of illumination the medium switches to a…

In a sub-excitable light-sensitive Belousov-Zhabotinsky chemical medium an asymmetric disturbance causes the formation of localized traveling wave-fragments. Under the right conditions these wave-fragment can conserve their shape and…