Related papers: Nonlinear acoustic waves in channels with variable…
The Dirichlet p-Laplacian in tubes of arbitrary cross-section along infinite curves in Euclidean spaces of arbitrary dimension is investigated. First, it is shown that the gap between the lowest point of the generalised spectrum and the…
A symmetry classification of possible interactions in a diatomic molecular chain is provided. For nonlinear interactions the group of Lie point transformations, leaving the lattice invariant and taking solutions into solutions, is at most…
An acoustic wave equation for pressure accounting for viscoelastic attenuation is derived from viscoelastic equations of motion. It is assumed that the relaxation moduli are completely monotonic. The acoustic equation differs significantly…
We consider a parabolic partial differential equation that can be understood as a simple model for crowds flows. Our main assumption is that the diffusivity and the source/sink term vanish at the same point; the nonhomogeneous term is…
Group classification of a class of nonlinear fin equations is carried out exhaustively. Additional equivalence transformations and conditional equivalence groups are also found. They allow to simplify results of classification and further…
Building up on classical linear formulations, we posit that a broad class of problems in signal synthesis and in signal recovery are reducible to the basic task of finding a point in a closed convex subset of a Hilbert space that satisfies…
Methods of Lie group analysis of differential equations are extended to weak solutions of (linear and nonlinear) PDEs, where the term ``weak solution'' comprises the following settings: (a) Distributional solutions. (b) Solutions in…
We study the steady uniphase and multiphase solutions of the discretized nonlinear damped wave equation.Conditions for the stability abd instability of the steady solutions are given;in the instability case the linear stable and unstable…
Classically, anisotropic surface wave tomography is treated as an optimisation problem where it proceeds through a linearised two-step approach. It involves the construction of 2D group or phase velocity maps for each considered period,…
Although acoustics is one of the disciplines of mechanics, its "geometrization" is still limited to a few areas. As shown in the work on nonlinear propagation in Reissner beams, it seems that an interpretation of the theories of acoustics…
For general anisotropic linear elastic solids with smooth boundaries, Rayleigh-type surface waves are studied. Using spectral factorizations of matrix polynomials, a self-contained exposition of the case of a homogeneous half-space is given…
This paper is concerned with the final value problem for a system of nonlinear wave equations. The main issue is to solve the problem for the case where the nonlinearity is of a long range type. By assuming that the solution is spherically…
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
A non-linear model associated with a Landau-Ginzburg-like behavior in mean field approximation forecasts phase transition waves and solitary kinks near the critical point. The behavior of isothermal waves is different of the one of…
In this paper, a general model of wireless channels is established based on the physics of wave propagation. Then the problems of inverse scattering and channel prediction are formulated as nonlinear filtering problems. The solutions to the…
We review recent progress in the dynamics of nonlinear lattice waves in heterogeneous media, which enforce complete wave localization in the linear wave equation limit, especially Anderson localization for random potentials, and Aubry-Andre…
We found universal anizopropic spectra of acoustic turbulence with the linear dispersion law \bbox{$\omega (k) =ck$} within the framework of generalized kinetic equation which takes into account the finite time of three-wave interactions.…
Spectral singularities and the coherent perfect absorption are two interrelated concepts that have originally been introduced and studied for linear waves interacting with complex potentials. In the meantime, the distinctive asymptotic…
This article is devoted to the analysis of a modified Davey-Stewartson system in three space dimensions, which was obtained in plasma physics for propagation of nonlinear dust acoustic waves. The system differs from the Davey-Stewartson…
We consider a nonlinear microcavity separating a waveguide channel into two parts so as the coupling between them is possible only due to the resonant properties of the microcavity. We provide a rigorous derivation of the equations used in…