ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

Nonlinear Waves. Solitons. Autowaves. Self-Organization.

Nonlinear waves of the sine-Gordon equation in the model with three attracting impurities

Purpose of this work is to use analytical and numerical methods to consider the problem of the structure and dynamics of coupled localized nonlinear waves in the sine-Gordon model with impurities (or spatial inhomogeneity of the periodic potential).

Excitation by shot circuited coaxial transducer of magnetostatic modes in rectangular yttrium iron garnet film

The purpose of this work is the study of design of new short-circuited coaxial transducer with thin linear jumper, that circuites on both sides of the grounded coaxial cylinder, located above the rectangular iron-yttrium garnet (YIG) film, in homogeneous constant magnetic field with rectangular film along its length or width. The thin linear jumper is directed parallel to the width of the YIG film. Methods. In the CST Microwave Studio environment, an electrodynamic analysis of the model was carried out using the finite element method.

Spectrum of exchange spin waves in a one-dimensional magnonic crystal with antiferromagnetic ordering

Purpose of the study is to show that the conditions for the propagation of exchanged spin waves (ESWs) in an asymmetric superlattice with antiferromagnetically ordered cells depend significantly on the chirality of the precession of the ESW magnetization (polarization, “magnon pseudospin”). Method. When constructing the EWS spectra, the Croning– Penny model (transfer-matrix method) and the Landau–Lifshitz equation are used to determine the nature of the waves in the cells.

Selection of spatial modes in an ensemble of non-locally coupled chaotic maps

Purpose of this work is to determine regularities of formation of spatial structures in an ensemble of chaotic systems with non-local diffusion couplings and to study how these structures depend on the wave response of the digital filter formed by the ensemble couplings structure. Methods. The study was carried out by numerical simulation of an ensemble of logistic maps, calculation of its typical oscillatory regimes and their spectral analysis. The network was considered as a digital filter with a frequency response depending on the coupling parameters.

Influence of parameters inhomogeneity on the existence of chimera states in a ring of nonlocally coupled maps

The aim of the research is to study the influence of inhomogeneity in a control parameter of all partial elements in a ring of nonlocally coupled chaotic maps on the possibility of observing chimera states in the system and to compare the changes in regions of chimera realization using different methods of introducing the inhomogeneity. Methods.

Effect of probing signal on the output signals spectrum of nonlinear spin waves in a cross based on waveguides of iron-yttrium garnet film

Subject. A change in the spectrum of spin waves (SW) in a magnetic cross is investigated when two signals pass through it: a pump signal and a probe signal. Objective. Detection of specific features in formation of the spectra of the output signals of SW in the multiport structure based on a yttrium iron garnet (YIG) film in the case of excitation of two magnetostatic surface waves (MSSW) simultaneously by the input antenna, where the first, with power higher than the first-order parametric instability threshold is the pump, and the second one is a probe. Methods.

Influence of noise on spiral and target wave regimes in two-dimensional lattice of locally coupled maps

 Abstract. The objective is to study numerically the dynamics of two-dimensional lattice of locally coupled maps of Rulkov. We analyze conditions for the appearance and existence as well as the properties of auto-wave spatio-temporal structures which are represented by spiral and target waves. The influence of noise on the lattice dynamics is explored as the noise intensity and the size of the noise-disturbed region are varied. Methods. In numerical experiments the evolution of the lattice dynamics is directly determined by the corresponding recurrence relations.

Reduced cumulant models for macroscopic dynamics of Kuramoto ensemble with multiplicative intrinsic noise

The purpose of this work is developing reduced models describing the macroscopic dynamics of the Kuramoto ensemble with multiplicative intrinsic noise on the basis of the method of circular cumulants. Methods. The dynamics of the system is considered within the framework of the phase reduction. The dynamics equations are obtained by the method of circular cumulants. Stability of the asynchronous state is considered on the basis of linear analysis. Results are verified by the numerical simulation. Results.

Micromagnetic modeling of self-focusing effect of backward volume magnetostatic waves in iron-yttrium garnet films

 Abstract. Topic. Micromagnetic modeling of the propagation of backward volume magnetostatic waves (MSBVW) beams, excited by an antenna, placed in the center of yttrium iron garnet (YIG) film, has been carried out. Aim. To explore MSBVWbeam focusing with an increase in the amplitude of the exciting field at the antenna under conditions when only four-magnon (4M) processes are allowed for the MSBVW. Methods. The problem was solved using micromagnetic modeling by the finite-difference method solving the Landau–Lifshitz equation using the OOMMF software package. Results.

Instability of homogeneous state and two-domain spatiotemporal structures in reaction-diffusion systems with global coupling

The purpose of this work was to study the typical instability of a homogeneous state resulting in two-domain spatiotemporal patterns in reaction-diffusion systems with global coupling. Methods. The linear stage of instability was analyzed based on the method of separation of variables for a one-dimensional two-component system of general form on a finite interval with Neumann boundary conditions. The development of instability at the nonlinear stage was simulated numerically using the method of lines for specific systems. Results.