斑图形成与孤子

We theoretically study the properties of one-dimensional nonlinear saturable photonic lattices exhibiting multiple mobility windows for stationary solutions. The effective energy barrier decreases to a minimum in those power regions where a…

We apply the averaging method to analyze spatio-temportal structures in nonlinear Schr\"odinger equations and thereby study the dynamics of quasi-one-dimensional collisionally inhomogeneous Bose-Einstein condensates with the scattering…

Ion traps are a versatile tool to study nonequilibrium statistical physics, due to the tunability of dissipation and nonlinearity. We propose an experiment with a chain of trapped ions, where dissipation is provided by laser heating and…

We present global existence results for solutions of reaction-diffusion systems on evolving domains. Global existence results for a class of reaction-diffusion systems on fixed domains are extended to the same systems posed on spatially…

We consider a finite number of coupled oscillators as an adaptation of the Kuramoto model of populations of oscillators. The synchronized solutions are characterized by an integer $m$, the winding number, and a second integer $l$.…

Time-periodic solitons of the parametrically driven damped nonlinear Schr\"odinger equation are obtained as solutions of the boundary-value problem on a two-dimensional spatiotemporal domain. We follow the transformation of the periodic…

In this paper, we investigate the complex dynamics of a spatial plankton-fish system with Holling type III functional responses. We have carried out the analytical study for both one and two dimensional system in details and found out a…

We address the properties of defect solitons (DSs) in defective parity-time potentials with real part of dual-frequency lattices. The impact of defect on stability regions of DSs was considered. For positive defects, DSs whose…

I investigate the problem of finding a statistical description of a complex many-body system whose invariant measure cannot be constructed stemming from classical thermodynamics ensembles. By taking solitons as a reference system and by…

We have introduced a class of spiraling elliptic solitons in generic nonlocal nonlinear media. The spiraling elliptic solitons carry the orbital angular momentum. This class solitons are stable for any degree of nonlocality except for the…

The nonlinear Schr\"{o}dinger equation with a linear periodic potential and a nonlinearity coefficient $\Gamma$ with a discontinuity supports stationary localized solitary waves with frequencies inside spectral gaps, so called surface gap…

We consider the onset of Boussinesq convection in a horizontal layer of electrically conducting incompressible fluid with rigid electrically insulating horizontal boundaries. The fluid is heated from below and rotates about a vertical axis;…

A theoretical scheme for an experimental implementation involving bisolitonic matter waves from an attractive Bose-Einstein condensate, is considered within the framework of a non-perturbative approach to the associate Gross-Pitaevskii…

We investigate nonlinear localized modes at light-mass impurities in a one-dimensional, strongly-compressed chain of beads under Hertzian contacts. Focusing on the case of one or two such "defects", we analyze the problem's linear limit to…

The surface pattern formation on a gelation surface is analyzed using an effective surface roughness. The spontaneous surface deformation on DiMethylAcrylAmide (DMAA) gelation surface is controlled by temperature, initiator concentration,…

We report the controllability of a gelation surface pattern formation. Recently, we have found and studied a novel kind of pattern formation that occurs during a radical polymerization (gelation) process. The pattern formation is observed…

We consider a Josephson junction system installed with a finite length inhomogeneity, either of microresistor or of microresonator type. The system can be modelled by a sine-Gordon equation with a piecewise-constant function to represent…

Directed motion of domain walls (DWs) in a classical biaxial ferromagnet placed under the influence of periodic unbiased external magnetic fields is investigated. Using the symmetry approach developed in this article the necessary…

Icicles form when cool water drips from an overhanging support under ambient conditions which are below freezing. Ice growth is controlled by the removal of latent heat, which is transferred into the surrounding air via a thin film of water…

We derive and justify a normal form reduction of the nonlinear Schrodinger equation for a general pitchfork bifurcation of the symmetric bound state that occurs in a double-well symmetric potential. We prove persistence of normal form…