This trend of physical acoustics was successfully developed at the IAP RAS on the foundation laid by the works made by L. A. Ostrovsky and his disciples in the 1970—1980s. Theoretical and experimental studies on this topic are substantially due to a rapid development of the physics of nonlinear wave phenomena as a whole, and the formation of nonlinear acoustics was parallel with the development of nonlinear optics and nonlinear plasma physics at the IAP RAS. The "classical" subject of the study performed at that time was the nonlinear effects in liquids with gas bubbles, which are a typical example of a structurally inhomogeneous medium containing inhomogeneities (air bubbles) with acoustic properties strongly different from those of the medium-matrix (liquid). As distinct from a weak nonlinearity of homogeneous liquids, caused by the intermolecular interaction, such media have a strong acoustic nonlinearity due to a strong compressibility of bubbles. Observation of the nonlinear effects caused by bubbles can be effectively used for their diagnostics even at very low concentrations of gas, which already indicates the potential of improving the sensitivity of nonlinearly acoustic diagnostics of media with "soft" inhomogeneities of the structure.

Structurally induced variations in elasticity modulus and quadratic nonlinearity parameter of a microinhomogeneous medium having defects with a relative softness parameter of 10—4 (typical of cracks). It is seen that the nonlinearity of the sample begins to rapidly increase (by the level of defect concentration) much earlier than the linear modulus variations

Since the end of the 1980s and especially from the beginning of the 2000s, great attention was paid to studying the microstructure-induced nonlinear effects in solids, e.g., in rocks, polycrystalline metals, construction materials, etc. These materials having typical structural peculiarities, such as microcracks, dislocations, and intergranular boundaries and contacts, also acquire distinct nonlinear acoustic properties. These properties are essentially different from the atomic nonlinearity of monocrystals and homogeneous amorphous bodies both in values of the effects and in character of their manifestations in specific media and materials. Besides the general physical interest, an investigation of such nonlinear effects is challenging due to the radically new possibilities of diagnostics for some important applications, e.g., in material science and nondestructive testing.
A large series of experimental and theoretical studies, many of which were the pioneering ones, was carried out at the IAP RAS to identify the physical mechanisms of a strong (anomalous) acoustic nonlinearity of media having an inhomogeneous microstructure. As a result, high-sensitivity nonlinear acoustic methods for nondestructive control and testing, methods for their industrial application, and appropriate diagnostic instrument prototypes have been developed (V. E. Nazarov, L. A. Ostrovsky, I. A. Soustova, A. M. Sutin, V. Yu. Zaitsev, I. Yu. Belyaeva, A. V. Radostin, L. A. Matveev, and V. V. Kazakov). The physical and rheological models of microinhomogeneous media elaborated at the IAP RAS show that the presence of even very low concentrations of highly compressible defects (e.g., cracks) leads to a strong increase in nonlinearity of the material with an almost constant value of the linear elastic moduli. This basic property can be used for an early (at the stage of initiation) detection of such defects in the samples and engineering constructions, while the conventional linear methods of acoustic testing almost fail. An application of these results, tested in the industrial environment, can be the technology of fatigue crack detection in the axles of railway wheel sets, which was developed in collaboration with the Nizhny Novgorod Branch of the Research Institute of Railway Transport.

Acoustic monitoring of the avalanche instability in a model granular medium with increased sloping angle of its surface. A sharp increase in level of the nonlinear generated signal component demonstrates the emergence of avalanche precursors at almost the same level of the primary wave

A series of laboratory and field experiments was carried out to explore numerous nonlinear acoustic effects in various (natural and artificial) microinhomogeneous media, such as the generation of difference frequency and higher harmonics, the nonlinear limitation of amplitude and self-induced transparency, the self-demodulation and nonlinear pulse delay, the amplitude and phase self-action, the amplitude cross-modulation of two interacting waves, the nonlinear shift of the resonance frequency, the slow dynamics of acoustically activated samples, and the manifestations of dilatatancy, polarization anisotropy, and dispersion of nonlinearity.

Method for nonlinear modulation diagnostics of microcracks in the axles of railway wheel sets. Left — contrast of normal (lower-order) modulation components for an axle with a crack (red color) and for an axle without defect (green color). Right — an additional increase in contrast of recognizing a sample without defects (a) and a sample with an initiating defect (b) by extracting higher-order modulation components (green color) against normal modulation components (black color)

One of the recent results in this field is associated with nonlinear geophysical acoustics. The use of high-power coherent sources allowed one for the first time to find the nonlinear effects of Raman scattering and self-action of seismic waves under natural conditions, which indicates the prospects for developing the nonlinear methods for diagnostics and monitoring of the rock state. The nonlinear approach to diagnostics of loose granular media also opens up new possibilities for monitoring of avalanche instabilities in such media. To clarify the nonlinear effect of seismic noise modulation by tidal deformations of the Earth's crust (discovered over 30 years ago), a physical mechanism substantiating the empirical use of some peculiarities of this effect as a sign of approaching strong earthquakes was proposed for the first time in cooperation with the Kamchatka Branch of the Geophysical Service of RAS.