斑图形成与孤子

Surface soliton formation and lattice soliton dynamics at an interface between two inhomogeneous periodic media are studied in terms of an effective particle approach. The global reflection, transmission and trapping characteristics are…

We study localized modes on a single magnetic impurity positioned in the bulk or at the surface of a one-dimensional chain, in the presence of a magnetic field $B$ acting at the impurity site. The strong on-site nonlinear interaction $U$…

In this letter we discuss a method for generating synchrony-optimized coupling architectures of Kuramoto oscillators with a heterogeneous distribution of native frequencies. The method allows us to relate the properties of the coupling…

We consider a damped $\beta$-Fermi-Pasta-Ulam chain, driven at one boundary subjected to stochastic noise. It is shown that, for a fixed driving amplitude and frequency, increasing the noise intensity, the system's energy resonantly…

In the absence of nonlinearity all normal modes (NMs) of a chain with disorder are spatially localized (Anderson localization). We study the action of nonlinearity, whose strength is ramped linearly in time. It leads to a spreading of a…

We report numerical simulations of one-dimensional cellular solutions of the stabilized Kuramoto-Sivashinsky equation. This equation offers a range of generic behavior in pattern-forming instabilities of moving interfaces, such as a host of…

The influence of time delay in systems of two coupled excitable neurons is studied in the framework of the FitzHugh-Nagumo model. Time-delay can occur in the coupling between neurons or in a self-feedback loop. The stochastic…

We consider the problem of initiation of a propagating wave in a one-dimensional excitable fibre. In the Zeldovich-Frank-Kamenetsky equation, a.k.a. Nagumo equation, the key role is played by the "critical nucleus'' solution whose stable…

We present exact numerical solutions in the form of spatially localized three-dimensional (3D) nonrotating and rotating (azimuthon) multipole solitons in the Bose-Einstein condensate (BEC) confined by a parabolic trap. We numerically show…

We study localized traveling waves and chaotic states in strongly nonlinear one-dimensional Hamiltonian lattices. We show that the solitary waves are super-exponentially localized, and present an accurate numerical method allowing to find…

We analyze localization of light at the interface separating square and hexagonal photonic lattices, as recently realized experimentally in two-dimensional laser-written waveguide arrays in silica glass with self-focusing nonlinearity [A.…

We investigate the dynamics of a gas of non-interacting particle-like soliton waves, demonstrating that phase transitions originate from their collective behavior. This is predicted by solving exactly the nonlinear equations and by…

We analyze the periodically forced Kuramoto model. This system consists of an infinite population of phase oscillators with random intrinsic frequencies, global sinusoidal coupling, and external sinusoidal forcing. It represents an…

Phase separation under directional quenching has been studied in a Cahn-Hilliard model. In distinct contrast to the disordered patterns which develop under a homogeneous quench periodic stripe patterns are generated behind the quench front.…

Electroconvection in a thin, sheared fluid film displays a rich sequence of bifurcations between different flow states as the driving voltage is increased. We present a numerical study of an annular film in which a radial potential…

The Degasperis-Procesi equation with self-consistent sources(DPESCS) is derived. The Lax representation and the conservation laws for DPESCS are constructed. The peakon solution of DPESCS is obtained.

We present a unified approach for qualitative and quantitative analysis of stability and instability dynamics of positive bright solitons in multi-dimensional focusing nonlinear media with a potential (lattice), which can be periodic,…

Turbulence of scroll waves is a sort of spatio-temporal chaos that exists in three-dimensional excitable media. Cardiac tissue and the Belousov-Zhabotinsky reaction are examples of such media. In cardiac tissue, chaotic behaviour is…

We revisit the problem of the three-soliton collisions in the weakly perturbed sine-Gordon equation and develop an effective three-particle model allowing to explain many interesting features observed in numerical simulations of the soliton…

Modulational instability in a photorefractive medium is studied in the presence of two wave mixing. We then propose and derive a model for forward four wave mixing in the photorefractive medium and investigate the modulational instability…