Related papers: Nonlinear transverse waves in deformed dispersive …
We study a non-linear convective-diffusive equation, local in space and time, which has its background in the dynamics of the thickness of a wetting film. The presence of a non-linear diffusion predicts the existence of fronts as well as…
All solids, whether crystalline or disordered, support elastic wave propagation with a linear dispersion relation in the long-wavelength limit. These waves, corresponding to low-frequency phonons, feature a vibrational density of states…
Nonlinear wave propagation in large extra spatial dimensions (on and above $d=2$) is investigated in the context of nonlinear electrodynamics theories that depend exclusively on the invariant…
We study the propagation of small amplitude waves superimposed on a large static deformation in a nonlinear viscoelastic material of differential type. We use bulk waves and surface waves to address the questions of dissipation and of…
The nonlinear dynamics of pulses in a two-temperature collisionless plasma with formation of dispersion shock waves is studied. An analytical description is given for arbitrary form of an initial disturbance with smooth enough density…
In this letter we investigate the propagation of nonlinear pulses along the free surface of flexible metamaterials based on the rotating squares mechanism. While these metamaterials have previously been shown to support the propagation of…
Vector solitary waves are nonlinear waves of coupled polarizations that propagate with constant velocity and shape. In mechanics, they hold the potential to control locomotion, mitigate shocks and transfer information, among other…
Two-dimensional nonlinear gravity waves travelling in shallow water on a vertically sheared current of constant vorticity are considered. Using Euler equations, in the shallow water approximation, hyperbolic equations for the surface…
In this paper, we study the nonlinear dispersive waves including the rarefaction and dispersive shock waves in the discrete modified KdV equation through the numerical simulations of the dispersive Riemann problems. In particular, we…
Acoustic wave propagation in a one-dimensional waveguide connected with Helmholtz resonators is studied numerically. Finite amplitude waves and viscous boundary layers are considered. The model consists of two coupled evolution equations: a…
The nonlinear propagation of electrostatic solitary waves is studied in a collisionless electron-positron pair plasma consisting of adiabatic cool electrons, mobile cool positrons (or electron holes), hot suprathermal electrons described by…
We present a general result of transverse nonlinear instability of 1-d solitary waves for Hamiltonian PDE's for both periodic or localized transverse perturbations. Our main structural assumption is that the linear part of the 1d model and…
The evolution of thermomagnetic perturbations in the resistive state of superconductors is considered. A qualitative pattern of the formation and further development of nonlinear stationary structures that describe the final stage of…
Layered media can be used as acoustic filters, allowing only waves of certain frequencies to propagate. In soft magneto-active laminates, the shear wave band gaps (i.e., the frequency intervals for which shear waves cannot propagate) can be…
We study the behavior of perturbations in a compressible one-dimensional inviscid gas with an ambient state consisting of constant pressure and periodically-varying density. We show through asymptotic analysis that long-wavelength…
We study a chain of anharmonic springs with tunable power law interactions as a minimal model to explore the propagation of strongly non-linear solitary wave excitations in a background of thermal fluctuations. By treating the solitary…
We analyze the propagation of elastic waves in soft materials subjected to finite deformations. We derive explicit dispersion relations, and apply these results to study elastic wave propagation in (i) nearly incompressible materials such…
Solutions of nonlinear acoustic equations describing propagation of strong sound pulses with account of curvature of wave fronts in multi-dimensional geometry are obtained from simple physical considerations. The form of these solutions…
In this paper we study the invasion fronts of spatially periodic monotone reaction-diffusion systems in a multi-dimensional setting. We study the pulsating traveling waves that connect the trivial equilibrium, for which all components of…
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…