Related papers: Nonlinear evolution equations for degenerate trans…
We consider a nonlinear wave equation with nonconstant coefficients. In particular, the coefficient in front of the second order space derivative is degenerate. We give the blow-up behavior and the regularity of the blow-up set. Partial…
The equations governing atmospheric flows are nonlinear. Consequently, the hierarchy of cumulant equations is not closed. But because atmospheric flows are inhomogeneous and anisotropic, the nonlinearity may manifest itself only weakly…
We derive coupled propagation equations for ultrashort pulses in a degenerate three-wave mixing process in quadratic media, using approximations consistent with the slowly evolving wave approximation [T. Brabec and F. Krausz, Phys. Rev.…
We prove decay estimates for solutions to non-isotropic linear systems of wave equations. The defining feature of these estimates is that they depend only on the commutation properties of the system with the scaling vector field. As…
In this paper anisotropic and dispersive wave propagation within linear strain-gradient elasticity is investigated. This analysis reveals significant features of this extended theory of continuum elasticity. First, and contrarily to…
Motivated by recent theoretical and experimental interest in the spin and orbital angular momenta of elastic waves, we revisit canonical wave momentum, spin, and orbital angular momentum in isotropic elastic media. We show that these…
In nonlinear dynamical systems with highly nonorthogonal linear eigenvectors, linear non-modal analysis is more useful than normal mode analysis in predicting turbulent properties. However, the non-trivial time evolution of non-modal…
The non-perturbative curvature inhomogeneities induced by relativistic viscous fluids are not conserved in the large-scale limit. However when the bulk viscosity is a function of the total energy density of the plasma (or of the trace of…
Propagation of gravitational and acoustic plane waves in a flat universe filled with a general relativistic, homogeneous and isotropic, spatially flat continuum is studied. The continuum is described by analogues of nonrelativistic…
Looking at rational solid-fluid mixture theories in the context of their biomechanical perspectives, this work aims at proposing a two-scale constitutive theory of a poroelastic solid infused with an inviscid compressible fluid. The…
Probably yes, since we find a striking similarity in the spatio-temporal evolution of nonlinear diffusion equations and wave packet spreading in generic nonlinear disordered lattices, including self-similarity and scaling.
A general equation describing the resonant nonlinear mode-coupling among kinetic Alfv\'en waves (KAWs) is derived using nonlinear gyrokinetic theory, which can be applied to study the potentially strong spectral energy transfer of KAWs. As…
We investigate the nonlinear equations governing wave propagation across a metamaterial consisting of a cellular periodic structure hosting resonators with linear and cubic springs. The resulting system of two coupled equations with cubic…
We study coupled acoustic and plasma waves in piezoelectric semiconductor crystals of hexagonal symmetry. We focus on the so called shear-horizontal or antiplane motions with one mechanical displacement. A set of two dimensional equations…
A mechanism for asymmetric (nonreciprocal) wave transmission is presented. As a reference system, we consider a layered nonlinear, non mirror-symmetric model described by the one-dimensional Discrete Nonlinear Schreodinger equation with…
We consider evolution of wave pulses with formation of dispersive shock waves in framework of fully nonlinear shallow-water equations. Situations of initial elevations or initial dips on the water surface are treated and motion of the…
In this article, we investigate the effects of the interplay between quadratic and cubic nonlinearities on the propagation of elastic waves in periodic waveguides. Through this framework, we unveil an array of wave control strategies that…
We study elastic shear waves of small but finite amplitude, composed of an anti-plane shear motion and a general in-plane motion. We use a multiple scales expansion to derive an asymptotic system of coupled nonlinear equations describing…
A tube conveying a large amount of fluid with a free outlet does not sit still. We construct and analyze a nonlinear evolution equation describing such phenomena. Two types of boundary conditions at the inlet are considered, one for which…
We estimate the importance of the nonlinear terms in the Vlasov equation for the development of the unstable modes. The results allow to identify the region of wavelength where the linear evolution is justified.