L. A. Ostrovskii’s research while affiliated with Institute of Applied Physics, Russian Academy of Sciences and other places

Based on the approximated theory developed by the authors to describe the interaction of complex solitons that are formed by kinks, i.e., drops of fields of different polarity, the features of the dynamics of intense internal wave solitons are studied in the context of nonintegrable Choi-Camassa equations. These equations describe the evolution of long internal waves with arbitrary amplitudes in a two-layer fluid. Making allowance for the complex character of the limiting amplitude solitons made it possible to study the dynamics of their interaction as longitudinal (not pointlike) formations for the first time. A series of the features of soliton interaction caused by the complexity of their structure is discovered and explained. These include the appearance of solitary waves with opposite polarity in the collision process, anomalously large phase shifts, etc. The existence of these features is verified by numerical experiments in the context of internal wave models permitting the existence of complex solitons. Keywordsinternal waves–solitons–limiting amplitude–interaction of solitons–asymptotical approach–kinks

General approaches to solving the problem of nonlinear acoustic spectroscopy of defects in geomaterials are considered. Expressions that relate the nonlinear response (scattering at combination frequencies) to the position, orientation, and nonlinear characteristics of narrow cracks are obtained. The expressions describe a broad class of nonlinear interactions at a crack. The nonlinearity caused by the contact of uneven rough edges of a crack is analyzed in detail. The results of the analysis are compared with the results obtained earlier from considering micromechanical models and with experimental data. The satisfactory agreement between the theoretical and experimental values of Landau’s moduli suggests that the mechanism of contact nonlinearity may manifest itself in the process of fracture of polycrystalline rock, when narrow cracks with uneven edges are formed. Numerical examples demonstrate the possibility of determining the orientation and position of a narrow crack. The procedure of solving the problem of crack localization is illustrated by the example of a crack in a thin rod. The importance of taking into account the phase data in the determination of the crack coordinate is pointed out.

The application of resonant acoustic spectroscopy to rock, building materials, and materials with cracks is hindered by the substantial mechanical losses in these materials and by the overlapping of the individual resonance responses. The paper describes a method for the determination of the resonance frequencies in low-Q materials in the presence of a strong overlapping of resonances. The effect of cracks on the values of the resonance frequencies and Q factors is studied experimentally.

Measurements of nonlinear effects in ice are presented. Harmonics and subharmonics of the fundamental frequency were experimentally detected near a crack in ice excitated by harmonic vibration. This effect is proposed for crack diagnostics.

Solitary waves in one- and two-dimensional lattices with quadratic nonlinearity are considered both analytically and numerically. Solutions in the form of a soliton with large amplitude and velocity proportional to its square root are derived. It is found that the property of self-similarity of solitons is changed due to discreteness in comparison with the continuous case. Cylindrical soliton fronts propagating through quadratic and hexagonal lattices are also calculated, the former causing anisotropical distortion of the fronts even in the continuum limit, the latter remaining isotropic in this limit.

Models for the excitation of collective modes in a system of nonlinear classical oscillators, initially out of phase, are discussed. The oscillators may be coupled in a dissipative or conservative manner. The analysis is based on the results of recent studies dealing with the problem of the free excitation of a coherent pulse, analogous to "superradiance" in two-level quantum systems. Several physical examples from the realms of electrodynamics and acoustics are discussed. The processes discussed here may be thought of as chaos-order transitions, provided that "chaos" is understood not as a stochastic nature of an individual oscillator but as the absence of a coherent component in their collective field.