M. M. Bogdan

Soliton complex dynamics in strongly dispersive medium

Abstract The concept of soliton complex in a nonlinear dispersive medium is proposed. It is shown that strongly interacting identical topological solitons in the medium can form bound soliton complexes which move without radiation. This phenomenon is considered to be universal and applicable to various physical systems. The soliton complex and its “excited” states are described analytically and numerically as solutions of nonlinear dispersive equations with the fourth and higher order spatial or mixed derivatives. The dispersive sine-Gordon (dSG), double and triple sine-Gordon, and piecewise linear models are studied in detail. Mechanisms and conditions of the formation of soliton complexes, and peculiarities of their stationary dynamics are investigated. A phenomenological approach to the description of the complexes and the classification of all the possible complex states are proposed. Some examples of physical systems, where the phenomenon can be experimentally observed, are briefly discussed.

Radiationless Motion of One-Dimensional Solitons in Dispersive Medium

Twenty years ago K. Nakajima et al1, 2 observed a phenomenon of sine-Gordon soliton bunching in numerical and mechanical experiments. Both realizations of the sine-Gordon system were discrete versiens of the model. The similar phenomenon of a formation of the 4π-soliton from the two 2π-solitins was discovered later in a highly discrete Sine-Gordon system by M. Peyrard and M. Kruskal3. The numerical simulation of a radiationless motion of 4π-soliton was performed in detail and a phenomenological theory based on the qualitative assumption was presented.

Spin waves in easy-axis antiferromagnets with precessing domain walls

Equations for the antiferromagnetism vector are used to study the spectrum and scattering of spin waves on a domain wall with precessing spins in an easy-axis antiferromagnet with a constant magnetic field directed along the easy axis. It is shown that this kind of magnetic field can be completely eliminated from the equations of motion, so that they can be reduced to a Lorentz invariant form. The spectral problem for weak excitation of a precessing domain wall is solved and exact solutions are found for the linearized equations describing the propagation of spin waves in antiferromagnets with this kind of domain wall. An explicit expression is found for the reflection coefficient of spin waves from a domain wall as a function of the wave vectors of the incident and transmitted waves, along with its dependence on the spin wave frequency. The range of frequencies within which the spin waves are fully reflected is found and it is shown that the reflection coefficient falls off sharply above the upper limit ...

Spectrum of nonlinear excitations of modulated nanoclusters

The nonlinear dynamics of a chain of four coupled anharmonic oscillators with alternating frequency parameters is investigated. This system is treated as an elementary fragment of a discrete modulated nonlinear medium, in particular, a medium of magnetic and elastic nanoclusters and coupled optical waveguides. The stationary monochromatic oscillations of the system are investigated analytically and numerically, and a complete classification of them is carried out. The bifurcation diagram for such a system is obtained: the spectral dependences of the oscillation frequencies on the integral of the number of states are found. A detailed investigation of the bifurcation process for the appearance of an excitation which is an analog of the gap soliton in a finite-size modulated medium is carried out.

Nonlinear periodic waves solutions of the nonlinear self-dual network equations

The new classes of periodic solutions of nonlinear self-dual network equations describing the breather and soliton lattices, expressed in terms of the Jacobi elliptic functions have been obtained. The dependences of the frequencies on energy have been found. Numerical simulations of soliton lattice demonstrate their stability in the ideal lattice and the breather lattice instability in the dissipative lattice. However, the lifetime of such structures in the dissipative lattice can be extended through the application of ac driving terms.

Dynamics of bound soliton states in regularized dispersive equations

The nonstationary dynamics of topological solitons (dislocations, domain walls, fluxons) and their bound states in one-dimensional systems with high dispersion are investigated. Dynamical features of a moving kink emitting radiation and breathers are studied analytically. Conditions of the breather excitation and its dynamical properties are specified. Processes of soliton complex formation are studied analytically and numerically in relation to the strength of the dispersion, soliton velocity, and distance between solitons. It is shown that moving bound soliton complexes with internal structure can be stabilized by an external force in a dissipative medium then their velocities depend in a step-like manner on a driving strength.

Dynamical features of bound states of topological solitons in highly dispersive low-dimensional systems

The nonstationary dynamics and interaction of topological solitons (dislocations, domain walls, fluxons) in one-dimensional systems with high dispersion are investigated. Processes of soliton complex formation are studied analytically and numerically in relation to the strength of the dispersion, soliton velocity, and distance between solitons. It is demonstrated that stable bound soliton states with complex internal structure can propagate in a dissipative medium owing to their stabilization by external forces.

Bifurcation picture and stability of the gap and out-gap discrete solitons

The dynamics of a quaternary fragment of a discrete system of coupled nonlinear oscillators with modulated frequency parameters is investigated, and the stability of its gap and out-gap soliton-like excitations is studied.

Frustrated vortex in a two-dimensional antiferromagnet

The interaction of a magnetic vortex with the frustration created by a magnetic defect is investigated in a discrete Heisenberg model of a two-dimensional antiferromagnet with easy-plane anisotropic exchange. Numerical solutions are obtained for the static Landau-Lifshitz equations describing the spin distribution in a system with magnetic frustration and a vortex. It is found that the energy of the magnet is minimum in the case when the center of the vortex coincides with the position of the magnetic impurity. It is shown that as a result of the attraction between the vortex and frustration, a two-dimensional solitonic bound state localized at the magnetic defect—a frustrated vortex—arises in the magnet. The energy of such a vortex is lower than that of the free vortex, and this effect can be manifested in features of the behavior of the EPR linewidth in two-dimensional magnets.

Local negative magnetic permeability and possibility of observation of breather excitations in magnetic metamaterials

It is shown that the long-wave dynamics and magnetic properties of one-dimensional systems constructed of the inductively and capacitively coupled split-ring resonators are described by the regularized nonlinear dispersive Klein–Gordon equations. It is found that in such systems a high-frequency magnetic field excites dynamic solitons on a “pedestal”—stable breathers, oscillating in anti-phase with respect to the background of uniform oscillations, which means the existence of regions with a negative magnetic permeability in the system. If supplemented by a medium with negative permittivity, such a system forms a “left-handed” metamaterial in which the regions with the breather excitations are transparent to electromagnetic radiation. This makes it possible to observe them experimentally.