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- W4283593310 abstract "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." @default.
- W4283593310 created "2022-06-28" @default.
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- W4283593310 date "2022-08-01" @default.
- W4283593310 modified "2023-09-24" @default.
- W4283593310 title "Dispersive nonlinear acoustic waves" @default.
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- W4283593310 doi "https://doi.org/10.1016/j.wavemoti.2022.102990" @default.
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