Conditions of applicability of linear models describing the propagation of acoustic waves

The conditions for the applicability of linear models describing the interaction of sounding acoustic waves with vibrational and acoustic fields are considered. Parameters are introduced into the mathematical model to assess the degree of nonlinearity and determine their further application. Keywords: dispersion, rheological medium, monochromatic waves, spectral decomposition. [email protected]; [email protected]

Predicting Wind Wave Suppression on Irregular Long Waves

The applicability of the wind wave suppression model developed by Chen and Belcher (2000) to irregular wave environments is investigated in this study. Monochromatic and irregular wave environments were simulated in the W2 (Wind/Wave) laboratory at the University of Maine under varying wind speeds. The Chen and Belcher (2000) model accurately predicts the reduction of the energy density of the wind waves in the presence of the monochromatic waves as a function of wave steepness, but under predicts this energy dissipation for the irregular waves. This is due to the consideration of a single wave frequency in the estimation of the growth rate and wave-induced stress of the monochromatic waves. The same formulations for the growth rate and wave-induced stress cannot be applied to irregular waves because their spectra contain energy over a wide range of frequencies. A revised version of the model is proposed to account for the energy contained within multiple wave frequencies from the power spectra for the mechanically generated irregular waves. The revised model shows improved results when applied to irregular wave environments.

THE DYNAMIC DEFORMATION OF THREE-COMPONENT POROUS MEDIA

A mathematical model of the dynamic deformation of three-component elastic media saturated with liquid and gas, given by elastic moduli and coefficients characterizing the porosity and compressibility of the liquid and gas, is considered. Formulas for determining the propagation velocity of monochromatic waves in ternary porous media are obtained. The existence of three longitudinal waves depends on the discriminant of a cubic equation and the velocity ratio.

Asymptotics for the Nodal Components of Non-Identically Distributed Monochromatic Random Waves

We study monochromatic random waves on ${\mathbb{R}}^n$ defined by Gaussian variables whose variances tend to zero sufficiently fast. This has the effect that the Fourier transform of the monochromatic wave is an absolutely continuous measure on the sphere with a suitably smooth density, which connects the problem with the scattering regime of monochromatic waves. In this setting, we compute the asymptotic distribution of the nodal components of random monochromatic waves, showing that the number of nodal components contained in a large ball $B_R$ grows asymptotically like $R/\pi $ with probability $p_n>0$ and is bounded uniformly in $R$ with probability $1-p_n$ (which is positive if and only if $n\geqslant 3$). In the latter case, we show the existence of a unique noncompact nodal component. We also provide an explicit sufficient stability criterion to ascertain when a more general Gaussian probability distribution has the same asymptotic nodal distribution law.

Abundant fractional solitons to the coupled nonlinear Schrödinger equations arising in shallow water waves

In this work, the dynamics of wave phenomena modeled by (2[Formula: see text]+[Formula: see text]1)-dimensional coupled nonlinear Schrodinger’s equations with fractional temporal evolution is studied. The solutions of the equations are two monochromatic waves with nonlinear modulations that have almost identical group velocities. The unified approach along with the properties of the local M-derivative are used to obtain dark and rational soliton solutions. The restrictions on parameters ensure that these soliton solutions are persevering. Lastly, the influence of the fractional parameter upon the obtained results are evaluated and depicted through graphs.