斑图形成与孤子
By methods of numerical simulations the dynamics of interaction of radially symmetric Bellavin-Polyakov type topological vortex in (2+1)-dimensional O(3) nonlinear sigma model is investigated. Obtained numerically the model of topological…
Instabilities are common phenomena frequently observed in nature, sometimes leading to unexpected catastrophes and disasters in seemingly normal conditions. The simplest form of instability in a distributed system is its response to a…
We characterize the nonlinear stage of modulational instability (MI) by studying the long-time asymptotics of focusing nonlinear Schrodinger (NLS) equation on the infinite line with initial conditions that tend to constant values at…
Chimera states are dynamical patterns in networks of coupled oscillators in which regions of synchronous and asynchronous oscillation coexist. Although these states are typically observed in large ensembles of oscillators and analyzed in…
Under investigation in this paper is the higherorder nonlinear Schrodinger and Maxwell-Bloch (HNLSMB) system which describes the wave propagation in an erbium-doped nonlinear fiber with higher-order effects including the fourth-order…
We introduced a fifth-order partial differential equation as a generalization of Hirota-Satsuma coupled with KdV system. This equation is investigated based on tanh method. By applying the suitable independent variable in Hirota-Satsuma…
We study the AB system describing marginally unstable baroclinic wave packets in geophysical fluids and also ultra-short pulses in nonlinear optics. We show that the breather can be converted into different types of stationary nonlinear…
For a large number of real nonlinear equations, either continuous or discrete, integrable or nonintegrable, uncoupled or coupled, we show that whenever a real nonlinear equation admits kink solutions in terms of $\tanh \beta x$, where…
We present numerical analysis of steady states in a two-component (spinor) driven-dissipative quantum fluid formed by condensed exciton-polaritons in an annular optically induced trap. We demonstrate that an incoherent ring-shaped optical…
In the present paper we consider the dynamics of special class of modulated regimes emerging in the Klein-Gordon trimer. In particular, this study unveils the unique states of resonant energy transfer manifested by the regular energy…
The description of shock waves beyond the shock point is a challenge in nonlinear physics. Finding solutions to the global dynamics of dispersive shock waves is not always possible due to the lack of integrability. Here we propose a new…
In-plane nonlinear delocalized vibrations in uniformly stretched single-layer graphene (space group P6mm) are considered with the aid of the group-theoretical methods. These methods were developed by authors earlier in the framework of the…
Nonlinear wave formation and propagation on a complex network with excitable node dynamics is of fundamental interest in diverse fields in science and engineering. Here, we propose a new model of the Kuramoto type to study nonlinear wave…
Prolific interactions of nonlinear waves on a plane-wave background in an erbium-doped fiber system are unveiled, based on explicit coexistence conditions extracting from the general higher-order solution of a coupled nonlinear…
Nonlinear instabilities are responsible for spontaneous pattern formation in a vast number of natural and engineered systems ranging from biology to galaxies build-up. We propose a new instability mechanism leading to pattern formation in…
We consider a chain of torsionally-coupled, planar pendula shaken horizontally by an external sinusoidal driver. It has been known that in such a system, theoretically modeled by the discrete sine-Gordon equation, intrinsic localized modes,…
The dynamics of fronts, such as chemical reaction fronts, propagating in two-dimensional fluid flows can be remarkably rich and varied. For time-invariant flows, the front dynamics may simplify, settling in to a steady state in which the…
Coupled nonlinear oscillators can exhibit a wide variety of patterns. We study the Brusselator as a prototypical autocatalytic reaction diffusion model. Working in the limit of strong nonlinearity provides a clear timescale separation that…
The paper is devoted to a reaction-diffusion equation with doubly nonlocal nonlinearity arising in various applications in population dynamics. One of the integral terms corresponds to the nonlocal consumption of resources while another one…
We study nonlinear waves on a plane-wave background in an erbium-doped fiber system, which is governed by the coupled nonlinear Schr\"odinger and the Maxwell-Bloch equations. We find that prolific different types of nonlinear localized and…