斑图形成与孤子
We introduce a discrete lossy system, into which a double hot spot (HS) is inserted, i.e., two mutually symmetric sites carrying linear gain and cubic nonlinearity. The system can be implemented as an array of optical or plasmonic…
A continuum model for the dynamics of a single step with the strongly anisotropic line energy is formulated and analyzed. The step grows by attachment of adatoms from the lower terrace, onto which atoms adsorb from a vapor phase or from a…
We realize a nonlinear acoustic lens composed of a two-dimensional array of sphere chains interfaced with water. The chains are able to support solitary waves which, when interfaced with a linear medium, transmit compact pulses with minimal…
We introduce the simplest one-dimensional nonlinear model with the parity-time (PT) symmetry, which makes it possible to find exact analytical solutions for localized modes ("solitons"). The PT-symmetric element is represented by a…
This experimental study of driven intrinsic localized modes (ILMs) in an electronic circuit lattice with saturable nonlinearity follows the theoretical work of Hadzievski and coworkers. They proposed that a saturable nonlinearity could…
By applying an out-of-phase actuation at the boundaries of a uniform chain of granular particles, we demonstrate experimentally that time-periodic and spatially localized structures with a nonzero background (so-called dark breathers)…
We analyze pattern-formation scenarios in the two-dimensional (2D) complex Ginzburg-Landau (CGL) equation with the cubic-quintic (CQ) nonlinearity and a cellular potential. The equation models laser cavities with built-in gratings, which…
We study propagation and on-off switching of two colliding soliton sequences in the presence of second-order dispersion, Kerr nonlinearity, linear loss, cubic gain, and quintic loss. Employing a Lotka-Volterra (LV) model for dynamics of…
We report on the spin properties of bright polariton solitons supported by an external pump to compensate losses. We observe robust circularly polarised solitons when a circularly polarised pump is applied, a result attributed to phase…
Vast landscapes extending from southern Angola, Namibia, and South Africa exhibit localised barren patches of vegetation called fairy circles. They consist of isolated or randomly distributed circular areas devoid of any vegetation. They…
We study $n$-pulse interaction in fast collisions of $N$ solitons of the cubic nonlinear Schr\"odinger (NLS) equation in the presence of generic weak nonlinear loss. We develop a reduced model that yields the contribution of $n$-pulse…
Kink dynamics in the underdamped and strongly discrete sine-Gordon lattice that is driven by the oscillating force is studied. The investigation is focused mostly on the properties of the mode-locked states in the {\it overband} case, when…
The Camassa-Holm equation with linear dispersion was originally derived as an asymptotic equation in shallow water wave theory. Among its many interesting mathematical properties, which include complete integrability, perhaps the most…
Motivated by recent experimental and theoretical studies of fewparticle vortex clusters in Bose-Einstein condensates, we consider the ordinary differential equations of motion and systematically examine settings for up to N = 6 vortices. We…
We consider propagating, spatially localised waves in a class of equations that contain variational and non-variational terms. The dynamics of the waves is analysed through a collective coordinate approach. Motivated by the variational…
In the present work we revisit the issue of the self-trapping dynamical transition at a nonlinear impurity embedded in an otherwise linear lattice. For our Schr\"odinger chain example, we present rigorous arguments that establish necessary…
We present a laboratory study on the instability of internal wave attractors in a trapezoidal fluid domain filled with uniformly stratified fluid. Energy is injected into the system via standing-wave-type motion of a vertical wall.…
We investigate the possibility of obtaining chimera state solutions of the non-local Complex Ginzburg-Landau Equation (NLCGLE) in the strong coupling limit when it is important to retain amplitude variations. Our numerical studies reveal…
We consider radial sine-Gordon kinks in two, three and higher dimensions. A full two dimensional simulation showing that azimuthal perturbations remain small allows to reduce the problem to the one dimensional radial sine-Gordon equation.…
Bending of a shape-invariant optical beam is achieved so far along parabolic or circular curves. Borrowing ideas used in nonlinear optical communication, we propose such a bending along any preassigned curve or surface, controlled by the…