We present a brief overview of the theory of high-intensity nonlinear diffracting beams. Characteristic distortions of the profiles of acoustic waves, which are observed during the wave propagation, are described. The following features are pointed out. First, the positive and negative half periods of the original harmonic signal are differently distorted. The positive-pressure phase duration is shortened and its “amplitude” is increased. On the contrary, the region of negative pressure is somewhat extended and reduced in “amplitude.” Second, the profiles are shifted to the region of negative values of the “accompanying” time, i.e., the diffraction of a convex beam leads to a slight increase in its propagation velocity. In addition, the positive pressure in some range of distances may exceed the initial value. Low-frequency geometric dispersion leads to differentiation of the weak signal profile in the focal region and in the far zone, which leads to the disappearance of unipolar video pulses. A stationary wave composed of sections of a parabolic shape can be formed in the waist. The limiting values of acoustic pressure and wave intensity in the focus are estimated. Approximate mathematical methods and the models used in the calculation of the wave profiles are described.

A method for generating solutions of the Burgers equation, which describe the interaction of waves in a nonlinear dissipative medium with a linearly growing wavefront, is proposed. The exact solutions describing these interactions and symmetry properties of the equation are used. It is shown that the rising wavefront is able to compete with the dissipation and compress the signal in time. On the contrary, the wavefront with the decreasing steepness “stretches” the signal.

The interaction of a short pulse with three types of wave profiles in a nonlinear dissipative medium are described: a stationary shock front of finite width, a nonstationary forming front, and a “stationary” wave the profile of which contains a singularity. Exact solutions to the Burgers equation are used, which describe these interactions, as well as the symmetry properties of this equation.

Yurii Yur'evich Balega (on his 70th birthday), Bisikalo D.V., Valyavin G.G., Vlasyuk V.V., Zelenyi L.M., Ikhsanov N.R., Korablev O.I., Postnov K.A., Romanyuk I.I., Rudenko O.V., Filippova E.E., Cherepashchuk A.M., Shustov B.M.

In memory of Yurii Mikhailovich Romanovsky, Aksenteva M.S., Guria G.T., Ivanitskii G.R., Makarov V.A., Polezhaev A.A., Priezzhev A.V., Riznichenko G.Yu., Ritus V.I., Romanovsky M.Yu., Rudenko O.V., Sysoev N.N., Tuchin V.V.

The main phenomena and mathematical models of the theory of nonlinear dispersive acoustic waves are described. For the physical dispersion of the relaxation type, the form of the kernels of the integro-differential equation for several relaxation times and the continuous spectrum of such times is indicated. The possibility of obtaining simple equations for media with a finite "memory time" is indicated. As a medium with resonant dispersion, where the kernels have an oscillatory character, a liquid with gas bubbles is considered. The dispersion curves are analyzed. It is argued that the introduction of resonant elements into a homogeneous matrix is a special case of creating metamaterials with unusual nonlinear-dispersion properties. As an example of the geometric dispersion, important problems of nonlinear focusing are considered based on the Ostrovsky–Vakhnenko equation, which is interpreted here as the projection of the Khokhlov–Zabolotskaya equation onto the acoustic beam axis. When analyzing the nonlinear dispersion, it was indicated that in acoustics the dependence of the wave propagation velocity on the magnitude of the perturbation is a common phenomenon. It leads to a distortion of the wave profile in time, as well as to a deformation of the spatial shape of the beam — to effects like self-refraction. In acoustics, nonlinearities of odd degrees are encountered much less frequently than in optics; cubic nonlinearity is possessed, for example, by shear waves in solids. Nevertheless, it leads to original effects — the formation of trapezoidal sawtooth waves and unusual self-focusing. The article systematically presents both known and new results.

This brief abstract historical review consists of two parts. Linear and weakly nonlinear oscillations of bubbles in acoustic field are considered in the first part. Basic data are presented on the following unusual properties of gas–liquid medium: very low speed of sound; high scattering cross section and large wavelength at the resonant frequency in comparison with the bubble radius; and high Q factor, which is determined by the loss on sound emission. The equation for small induced oscillations in acoustic field and the dispersion equation for the compressibility of the medium are presented. It is indicated that the effective nonlinearity of the medium may exceed by three orders of magnitude the nonlinearities of both liquid and gas taken separately. Some applications of small oscillations of bubbles in hydroacoustics, medicine, and linear and nonlinear diagnostics are described. The phenomena of significant changes in the sizes of bubbles, including their creation and collapse, are discussed in the second part. The sonoluminescence of a group of bubbles and a single bubble is described. Some facts related to the unbounded cumulation and its limiting factors are indicated. The history of attempts to implement “sonofusion” (thermonuclear reaction under collapse of cavitation bubbles) is outlined.

Radiation force is a universal phenomenon in any wave motion where the wave energy produces a static or transient force on the propagation medium. The theory of acoustic radiation force (ARF) dates back to the early 19th century. In recent years, there has been an increasing interest in the biomedical applications of ARF. Following a brief history of ARF, this article describes a concise theory of ARF under four physical mechanisms of radiation force generation in tissue-like media. These mechanisms are primarily based on the dissipation of acoustic energy of propagating waves, the reflection of the incident wave, gradients of the compressional wave speeds, and the spatial variations of energy density in standing acoustic waves. Examples describing some of the practical applications of ARF under each mechanism are presented. This article concludes with a discussion on selected ideas for potential future applications of ARF in biomedicine.

specialist in the field of acoustoelectronics, acousto-optics, semiconductor physics, optoelectronics, and the theory of weak signal recording, a member of the Bureau of the Division of Nanotechnology and Information Technology of the Russian Academy of Sciences (RAS), a laureate of 5 (!) USSR and Russian Federation State Prizes, an academician of RAS, and a doctor of physical and mathematical sciences, Vladislav Ivanovich Pustovoit, passed away on July 5, 2021 at the age of 85. V I Pustovoit was born on November 15, 1936 in Berdyansk (Dnepropetrovsk region, Ukrainian SSR, now Zaporizhzhya region, Ukraine). In 1959, he graduated from Dnepropetrovsk State University, and in 1963 from the postgraduate course of Lebedev Physical Institute of the USSR Academy of Sciences (FIAN) (Theoretical Department). In that same year, V I Pustovoit defended his candidate thesis, titled ``The Theory of Low-Frequency Wave Amplification in Semiconductors and Dense Plasma in the Presence of Drift.'' The thesis had been prepared under the guidance of Academician Vitaly Lazarevich Ginzburg (later the laureate of the 2003 Nobel Prize in physics). In 1972, Vladislav Ivanovich defended his doctoral thesis, ``A Theory of Acoustic Wave Propagation, Amplification, and Generation in Semiconductors.'' In 1973, he was conferred the rank of professor, in 1990 he was elected a corresponding member of the USSR Academy of Sciences, and in 2006 became a full member of RAS in the Division of Informational Technologies and Computational Systems with the specialty `scientific instrument engineering.' In acoustoelectronics, V I Pustovoit, together with Yu V Gulyaev, suggested, for the first time in the world, the ideas of acoustic wave amplification. They laid the basis for a powerful direction of science and technology, which all over the world is currently referred to as acoustoelectronics. Now, it is the field of solid state physics and the technological basis of the new generation of functional devices of ultrafast energy-dependent information processing. In acousto-optics, he solved problems regarding light diffraction by inhomogeneous acoustic waves and waves with sharp phase modulation in crystals. These physical models fostered the creation of new, more precise methods of spectral measurements using acousto-optic spectrometers. His ideas concerning collinear light diffraction by sound waves in crystals led to the creation of production of a whole family of quickly tunable optical filters and spectrometers in the UV, visible, and IR ranges, now called acoustooptic spectrometers. After finishing the postgraduate course at FIAN, V I Pustovoit began working at the All-Russian Scientific Research Institute for Physical-Engineering and Radiotechnical Metrology (VNIIFTRI). This gave birth to the scientific potential, which then led to considerable scientific and productive achievements. An original technology for producing acousto-optical elements was developed and applied in industry under the guidance of V I Pustovoit and with his direct participation; acousto-optic (AO) onboard (space, air, and marine) optical radiation spectrometers in the visible and IR ranges with record characteristics in spectral resolution, light-generating power, and operating speed were created on the basis of this technology for the first time in the world; AO systems of plasmachemical process control in the production of giant-size integral systems were created and implemented; specialized acousto-optical laser systems for the simultaneous transmission of large information arrays through optical communication links were designed. Investigated with the participation of V I Pustovoit and under his guidance was diffraction of light and X-ray radiation by acoustic waves in crystals with allowance for optical and acoustic anisotropy and the electron band structure. This made it possible to propose and create AO processors in the frequency range of 107ÿ1010 Hz for a fast Fourier expansion of radio signals in real time and for Uspekhi Fizicheskikh Nauk 191 (8) 899 ± 900 (2021) Translated by M V Tsaplina PERSONALIA PACS number: 01.60.+q

In this paper, we describe a diagnostic method based on “acoustic weighing” of sheet materials. The defect mass or mass deficit determines the frequency shift of the oscillating membrane. The measuring device of Academician N.N. Andreev invented in 1925 and based on the effect of “rattling” due to the “bouncing” of a small weight lying on a telephone membrane is described. The harmonics that appear at sufficiently large oscillation amplitudes are calculated. It is shown that harmonics can also appear during the operation of modern high-precision instruments, for example, tunneling and atomic force microscopes.

Rabinovich, professor, doctor of phys.-math. sciences, an outstanding theoretical physicist, and a corresponding member of the Russian Academy of Sciences (RAS). M I Rabinovich was born on 20 April 1941 in Nizhny Novgorod into the family of the well-known chemist Izrail Beniaminovich Rabinovich. M I Rabinovich (or MIR, as his disciples and friends call him) belongs to the third generation of the renowned scientific school for nonlinear oscillations and waves founded by Academician A A Andronov and based atGorky State University (GSU). In 1962, immediately after he graduated from the Radiophysical Faculty of GSU, he began teaching at the Department of Theory of Oscillations. In 1967, Mikhail Izrailevich defended his Ph.D. thesis, ``Self-oscillations of distributed systems,'' under the guidance of A A Andronov's disciple A V Gaponov-Grekhov. In this thesis and in later studies (included in his D.Sc. thesis, which he defended in 1974 at the age of 33 in the `star' council of the Institute for Physical Problems), M I Rabinovich laid the basis of a new direction in nonlinear dynamicsÐ selfoscillating and autowave processes in distributed nonlinear nonequilibrium media. Solving problems from very different areas of physics and related sciences (nonlinear optics, plasma physics, hydrodynamics, biology, etc), M I Rabinovich continues to apply the theoretical oscillatory approach rooted in the classical work of A A Andronov. The asymptotical method for nonlinear distributed systems, developed by M I Rabinovich in collaboration with A A Rozenblum, belongs to the standard set of tools of nonlinear dynamics and theoretical physics. Many phenomena and effects discovered and investigated by him, namely, stationary autowaves, explosive instability, competition of modes, and localized autowave excitations, were later discovered or experimentally realized. Because of the Iron Curtain that separated the Soviet Union from the rest of the world till the late 1980s, many of M I Rabinovich's discoveries (for instance, stochastic synchronization) were not known abroad and were rediscovered later on. In spring of 1972, in a guest house on the bank of the river Oka, M I Rabinovich took an active part in the organization of the Gorky school for nonlinear waves (NWs)Ð the first in a line of such schools that were almost continuously held every two years and are being carried out to the present day (the 19th NW school took place in spring of 2020). These schools soon became famous all over Russia and attracted very prominent Russian physicists and mathematicians as lecturers, for example, V IArnold, E PVelikhov, AMZhabotinskii, Ya B Zel'dovich, B B Kadomtsev, O A Ladyzhenskaya, S PNovikov, SMRytov, RZSagdeev,RVKhokhlov, B V Chirikov, and many others. For many years, M I Rabinovich remained an irreplaceable organizer and a linchpin of these fortnight schools, famous not only for the highest scientific level, but also for the unique atmosphere of informal communication, high spirits, and sports. Not only was M I Rabinovich one of the brightest lecturers, but he also made great efforts to edit the school proceedings, by which one can readily follow the development of nonlinear physics in its `golden years'. When the Institute of Applied Physics (IAP) of the USSR Academy of Sciences (AS) was founded in 1977, M I Rabinovich became head of the Sector of Nonlinear Dynamics, where he had fruitfully combined scientific and organizational work for over 15 years. This transformation coincided with the beginning of studies on the chaos theory, and M I Rabinovich is deservedly considered to be one of the pioneers in this area. Widely known are the `Rabinovich system' and `Rabinovich±Fabrikant system', an electron