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

Nonlinear Waves. Solitons

The effect of parametric processes on the propagation of spin waves in cross-shaped structures based on waveguides from yttrium iron garnet films

Topic. In this work, we experimentally explore the spin waves (SW) propagation in tangentially magnetized cross-like structure in the shape of two orthogonal waveguides on the base of yttrium iron garnet (YIG) film for the conditions when the first order parametric processes take place. Aim.

The ring system with nonlinear elements, described by the two waves interaction model, manifesting the phenomena of complex analytical dynamics

This paper proposes a method of constructing of the ring system, in which the phenomena of complex analytical dynamics such as the Mandelbrot and Julia sets, are implemented in some approximation. The system is non-autonomous, includes frequency filters and nonlinear elements, described by the model of the resonant interaction of waves in quadratic nonlinear dispersive medium.

Passage of the magnetostatic wave propagating through the lattice on the basis of the magnon crystal

The paper presents the results related to the construction of a model based on the coupled waves to describe the characteristics of magnetostatic waves passing through the structure on the basis of one-dimensional magnon crystal at various geometric parameters of the structure and at finite values of the input power.

Mode localization in Fermi-Pasta-Ulam chains with arbitrary degree of nonlinearity

q-Breathers are exact periodic solutions of nonlinear acoustic chain systems, exponentially localized in the space of normal modes. Their presence determines the energy localization in initially excited modes, the absence of thermalization and persistence of quasi-linear spectrum. In the present paper we study the influence of the order of nonlinearity γ on the localization length in the q-space, delocalization threshold and scaling of these properties with the system size.

Nonlinear electromagnetic wave passing through the layer with quadratic and fractionally-­polynomial permittivity dependences on amplitude

The integral equations for powerful flat electromagnetic wave diffraction on nonlinear dielectric layer with cubic nonlinearity and fractionally­polynomial permittivity dependence on wave amplitude have been considered and solved. There are results which have been obtained by several numerical methods: series approaching, minimal discrepancy, power series expansion, and Runge–Kutt methods. Also the some analytical results are presented.

Kink dynamics in the discrete Klein–Gordon model with asymmetric potential in the presence of AC driving

A discrete Klein­Gordon model with asymmetric potential that supports kinks free of the Peierls­Nabarro potential (PNp) is constructed. Ratchet of kink under harmonic AC driving force is investigated in this model numerically and contrasted with the kink ratchet in the conventional discrete model where kinks experience the PNp. We show that the PNp­free kinks exhibit ratchet dynamics very much different from that reported for the conventional lattice kinks which experience PNp.

Characteristics of gap discrete breathers in crystals with NaCl structure

Molecular dynamics method is used to study the effect of mass ratio of anions and cations on the phonon spectra of the crystal with NaCl structure and on the discrete breathers existence  conditions and properties of gap discrete breathers. We show that discrete breathers can be easily excited for the mass ratio less than 0.2, when the gap in the phonon spectrum is wide enough to support them.

Solitons in two­-fluid magnetohydrodynamics with non­zero electron inertia

The interaction between solitary waves in two fluid magnetohydrodynamic model of plasma with electron inertia taken into account is investigated analytically and numerically. Waves with linear polarization of a magnetic field are considered. A principal difference of the present work is the using of the «exact» equations, instead of the modeling equations. It is numerically shown, that solitary waves really are solitons, i.e. their interaction is similar to interaction of colliding particles.

Introduction to discrete breathers theory

We make a basic review of the theory of discrete breathers – spatially localized solutions in nonlinear lattices. We describe the mathematical conditions and physical prerequisites of their existence and methods of their study by example of one-dimensional lattices. We consider localized solutions with infinite and finite lifetimes. We include some new results within the problems of discrete breather generation resulting from harmonic wave destruction and controlling the formation of rotational breather solutions by external forcing.

The leaky modes of multilayered waveguide with nonlinear dielectrics

Characteristics of the leaky modes, propagating along the planar layered waveguides with nonlinear media, are studied. The mode phase constants and attenuation coefficients are calculated. In nonlinear structures the dependencies of the mode field distributions on the longitudinal coordinate are shown to differ from exponential ones which are typical for the linear problems. This property results in the effect of the different modes transformation even for the regular geometry of the waveguide.

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