斑图形成与孤子
We study light localization at a phase-slip defect created by two semi-infinite mismatched identical arrays of coupled optical waveguides. We demonstrate that the nonlinear defect modes possess the specific properties of both nonlinear…
Reaction--diffusion equations with a fractional Laplacian are reduced near a long wave Hopf bifurcation. The obtained amplitude equation is shown to be the complex Ginzburg-Landau equation with a fractional Laplacian. Some of the properties…
Nonlinear evolution of a reaction--super-diffusion system near a Hopf bifurcation is studied. Fractional analogues of complex Ginzburg-Landau equation and Kuramoto-Sivashinsky equation are derived, and some of their analytical and numerical…
We study surface modes in semi-infinite chirped two-dimensional photonic lattices in the frame- work of an effective discrete nonlinear model. We demonstrate that the lattice chirp can change dramatically the conditions for the mode…
We demonstrate that necklace-shaped arrays of localized spatial beams can merge into stable fundamental or vortex solitons in a generic model of laser cavities, based on the two-dimensional complex Ginzburg-Landau equation with the…
The refraction is theoretically considered of ultimately short pulses at interface of two dielectrics that contains a thin film of nonlinear metamaterial. For the model of metamaterial composed of nanoparticles and magnetic nanocircuits…
Fluxon transmission through several impurities of different strength and type (i.e., microshorts and microresistors), placed in a long Josephson junction is investigated. Threshold pinning current on the impurities is computed as a function…
Motivated by recent proposals of ``collisionally inhomogeneous'' Bose-Einstein condensates (BECs), which have a spatially modulated scattering length, we study the existence and stability properties of bright and dark matter-wave solitons…
Granular surfaces tend to develop lateral ripples under the action of surface forces exerted by rolling wheels, an effect known as washboard or corrugated road. We report the results of both laboratory experiments and soft-particle direct…
The Fermi-Pasta-Ulam problem was one of the first computational experiments. It has stirred the physics community since, and resisted a simple solution for half a century. The combination of straightforward simulations, efficient…
Cold atoms in optical high-Q cavities are an ideal model system for long-range interacting particles. The position of two arbitrary atoms is, independent on their distance, coupled by the back-scattering of photons within the cavity. This…
Modifications of spatial distributions of dynamic magnetization corresponding to spinwave eigenmodes of magnetic squares subjected to a strong microwave excitation field have been studied experimentally and theoretically. We show that an…
Considering the coherent nonlinear dynamics in double square well potential we find the example of coexistence of Josephson oscillations with a self-trapping regime. This macroscopic bistability is explained by proving analytically the…
We consider the problem of the existence of a dynamical barrier of ``mass'' that needs to be excited on a lattice site to lead to the formation and subsequent persistence of localized modes for a nonlinear Schrodinger lattice. We contrast…
We study the combined effect of delayed Raman response and bit pattern randomness on pulse propagation in massive multichannel optical fiber communication systems. The propagation is described by a perturbed stochastic nonlinear…
We consider an extension of Kuramoto's model of coupled phase oscillators where oscillator pairs interact with different strengths. When the coupling coefficient of each pair can be separated into two different factors, each one associated…
Intrinsic localized modes (ILMs), also called discrete breathers, are directly generated via modulational instability in an array of coupled pendulums. These ILMs can be stabilized over a range of driver frequencies and amplitudes. They are…
We derive a family of singular iterated maps--closely related to Poincare maps--that describe chaotic interactions between colliding solitary waves. The chaotic behavior of such solitary wave collisions depends on the transfer of energy to…
We derive an analytic formula for the lateral dynamics of solitons in a general inhomogeneous nonlinear media, and show that it can be valid over tens of diffraction lengths. In particular, we show that solitons centered at a lattice…
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…