Arnold M. Kosevich

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.

Forced vibrations and resonance wave scattering on impurity in 1D discrete lattice with nearest- and next-nearest-neighbors interaction

Abstract Vibrations of a discrete linear atomic chain with nearest- and next-nearest-neighbor interaction consist of two parts corresponding to localized and extended vibrations. The vibrations under external force action are studied. It is shown that localized vibrations with discrete frequencies lying in the continous spectrum can arise and the condition for their existence is derived. The wave scattering from a point impurity is analysed. Resonance reflection of the doublepartial waves with frequencies belonging to the quasilocalized spectrum is described.

Density of quasilocalized states along the resonance curves in continuum

Densities of quasilocalized states are calculated and analyzed for a one-dimensional system with a point defect and an FCC crystal with a planar defect. The density of states displays a pronounced peak that is positioned near the energy (frequency) of resonant transmission of a particle (wave) through the defect but slightly shifted from this energy. The peak nears the resonance frequency and sharpens, tending to a δ function, as the continuum edge is approached.

Localized waves and peculiarities of acoustic phonon scattering from a plane defect in FCC crystal

Abstract Resonance peculiarities of phonon scattering from a plane defect in FCC crystal are described based on the lattice theory. The conditions for the total transmission of phonons are analyzed. A phenomenon of transformation of acoustic waves during the scattering is discussed.

Self-localized states as precursors to strong first-order structural phase transition

A phenomenological theory of precursor to strongly first-order structural phase transition is proposed. Temperature dependence of structural characteristics in the linear Hamiltonian results in nonlinearity, which shifts the phonon band and allows for self-localized states. The drastic increase in activation probability of a self-localized state can be interpreted as the precursor, rather than usual nucleation.

Pecularities of acoustic phonon scattering from a planar crystal defect and pseudosurface phonons (Resonant scattering of transverse phonons from a thin defect layer)

Abstract A scattering of acoustical phonons from a planar crystal defect is studied. A resonance reflection of the transverse phonons from the planar defect is discovered and conditions of such a reflection are investigated. It is shown that the resonance conditions are connected with existence of longitudinal phonons localized at the planar defect and travelling along it. The problem is analyzed basing both on the lattice dynamics and on the theory of elasticity. A non-symmetrical stationary solution which consists of (1) a homogeneous transverse wave propagating only in one elastic semispace and (2) longitudinal localized waves in the both elastic semispaces is found. The condition of the resonance reflection of the transverse phonons from the defect layer coincides with a condition under which the non-symmetrical stationary vibration exists. The influence of properties of the models considered on the resonance frequencies is discussed.