Nonlinear Waves. Solitons

Magnetostatic surface wave (MSSW) bright solitons in a ferrite-dielectric-metal FDM) structure have been studied experimentally and numerically in the framework of he nonlinear Schr¨ odinger equation. The attention was focused on the influence of the  parametric instability on the soliton formation and propagation. We also discussed the contribution of the non-solitary (dispersive wave) part of the MSSW pulse on the soliton propagation, to show that their mutual interference leads to the levelling off or to the appearance of some peaks in the MSSW pulse output vs the input amplitude.

First order (three-magnon) parametric instability of magnetostatic surface waves (MSSW) was experimentally studied in two-dimensional (2D) magnonic crystals with rhombic and square lattices with lattice parameter 37–40 mm. The instability was produced by etching of holes 32 mm in diameter and 1–2 mm in depth in the 16 mm-thick yttrium iron garnet (YIG) film. It was found, that MSSW threshold powers for parametric instability development in case of 2D magnonic crystals are of the order of two times greater than analogous threshold values for starting YIG films.

Chaotic dynamics in the systems of coupling nonautonomous van der Pol oscillators with resonance and nonresonance communicator of the signal is considered. For the both models phase map for the period of the external force are show hyperbolic attractor of the Smale–Williams type. In these models features of chaotic dynamics investigated depending on type of the communicator of the signal.

We study the stability of the symmetric and antisymmetric discrete breathers in the monoatomic chain described by potential energy which is a uniform function of the fourth order. It is shown that the change of the stability properties of these two dynamical objects (known as Sievers-Takeno and Page modes, respectively) takes place at the same strength of the inter-site interactions with respect to the on-site interactions. We also present a new method (the «pair synchronization» method) for the discrete breather construction in the arbitrary nonlinear Hamiltonian lattices.

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.

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.

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.

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.

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.

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.