Probability Distributions of the Riemann Wave and an Integral of It

Doklady Physics - In this paper, we study the statistical characteristics of the Riemann wave and the integral of it. Such problems arise in the physics of fronts’ propagation, in particular,...     

On Diffraction of a Sawtooth Nonlinear Wave by a Narrow Circular Aperture in a Screen

Acoustical Physics - The paper presents the experimental and theoretical studies of diffraction effects in intense acoustic beams diffracted by a narrow circular aperture in a screen. The...     

Bispectral analysis in inverse nonlinear acoustics problems

Using the spectral solution to the evolutionary Burgers equation, we have numerically simulated the propagation of intense random acoustic waves in a nondisperse medium. We have solved the problem of reconstructing the initial signal spectrum using the measured spectral and bispectral characteristics of the received signal on short tracks.     

Absorption of intense regular and noise waves in relaxing media

An integro-differential equation is written down that contains terms responsible for nonlinear absorption, visco-heat-conducting dissipation, and relaxation processes in a medium. A general integral expression is obtained for calculating energy losses of the wave with arbitrary characteristics—intensity, profile (frequency spectrum), and kernel describing the internal dynamics of the medium. It is shown that for weak waves, the general integral leads to well-known results of a linear approximation. Profiles of stationary solutions are constructed both for an exponential relaxation kernel and for other types of kernels. Energy losses at the front of week shock waves are calculated. General integral formulas are obtained for energy losses of intense noise, which are determined by the form of the kernel, the structure of the noise correlation function, and the mean square of the derivative of realization of a random process.     

Spectra of discontinuous noise waves

The article considers the problem of the transformation of the energy spectrum of an intense random wave in a nonlinear, nondisperse medium. It is assumed that at the inlet to the nonlinear medium there is given a random quasimonochromatic wave, and an investigation is made of the spectrum of a nonlinear wave at distances where the original continuous wave goes over into a sequence of sawtooth pulses with a random position of the discontinuity and with random amplitudes. In the work, an investigation was made of the dependence of the spectral characteristics of discontinuous noise waves on the statistics of the amplitude and phase of the input quasimonochromatic wave. The form of the spectrum of the wave is found at low frequencies, which appear due to the effect of the autodetection of the quasimonochromatic wave in a nonlinear medium. The effect of the viscosity of the medium on the form of the energy spectrum is also discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 21, No. 11, pp. 1627–1636, November, 1978.The authors are indebted to A. N. Malakhov and A. I. Saichev for their valuable evaluations.