Related papers: Dispersive effects in a scalar nonlocal wave equat…
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.
We prove wave breaking --- bounded solutions with unbounded derivatives --- in the nonlinear nonlocal equations which combine the dispersion relation of water waves and the nonlinear shallow water equations, and which generalize the Whitham…
The concept of spectrum for a class of non-linear wave equations is studied. Instead of looking for stability, the key to the spectral structure is found in the instability phenomena (bifurcations). This aspect is best seen in the…
A new class of solitary waves arises in the solution of nonlinear wave equations with constant impedance and no dispersive terms. They depend on a balance between nonlinearity and a dispersion-like effect due to spatial variation in the…
Effects of spatially varying interfacial parameters on the propagation of surface waves are studied. These variations can arise from inhomogeneities in coverage of surface active substances such as amphiphillic molecules at the fluid/gas…
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…
Elastic wave dispersion is studied in an octet truss lattice and compared with a designed rib lattice known to exhibit strong Cosserat elastic effects. Dispersion entails variation of wave speed with frequency. The phenomenon is…
We present a linear dispersive partial differential equation which manifests a number of qualitative features of dispersive shocks, typically thought to occur only in nonlinear models. The model captures much of the short time phenomenon…
In this paper we study the asymptotic behaviour of a nonlocal nonlinear parabolic equation governed by a parameter. After giving the existence of unique branch of solutions composed by stable solutions in stationary case, we gives for the…
We follow the dynamics of nonlinear waves in two-dimensional disordered lattices with tunable nonlinearity. In the absence of nonlinear terms Anderson localization traps the packet in space. For the nonlinear case a destruction of Anderson…
The novel concept of spectral diffusivity is introduced to analyse the dissipative properties of continua. The dissipative components of a linear system of evolution equations are separated into noninteracting parts. This separation is…
Nonlinear waves in a liquid with gas bubbles are studied. Higher order terms with respect to the small parameter are taken into account in the derivation of the equation for nonlinear waves. A nonlinear differential equation is derived for…
We study the statistical and dynamical behavior of turbulent Kelvin waves propagating on quantized vortices in superfluids, and address the controversy concerning the energy spectrum that is associated with these excitations. Finding the…
The work is inspired by thermo-and photoacoustic imaging, where recent efforts are devoted to take into account attenuation and varying wave speed parameters. In this paper we derive and analyze causal equations describing propagation of…
Internal gravity waves are an essential feature of stratified media, such as oceans and atmospheres. To investigate their dynamics, we perform simulations of the forced-dissipated kinetic equation describing the evolution of the energy…
Within periodic materials and structures, wave scattering and dispersion occur across constituent material interfaces leading to a banded frequency response. In an earlier paper, the elastodynamics of one-dimensional periodic materials and…
The evolution of the interface separating a conduit of light, viscous fluid rising buoyantly through a heavy, more viscous, exterior fluid at small Reynolds numbers is governed by the interplay between nonlinearity and dispersion. Previous…
This paper aims to investigate a multi-dimensional transport equation with nonlocal velocity and fractional dissipation.The balance between the nonlinearity and dissipation gives rise to three different cases, namely the subcritical,…
This note analytically investigates non-reciprocal wave dispersion in locally resonant acoustic metamaterials. Dispersion relations associated with space-time varying modulations of inertial and stiffness parameters of the base material and…
We study the propagation properties of the solutions of the finite-difference space semi-discrete wave equation on an uniform grid of the whole Euclidean space. We provide a construction of high frequency wave packets that propagate along…