Related papers: Oscillatory wave fronts in chains of coupled nonli…
We study the stability and dynamics of traveling-front solutions of a modified Kuramoto--Sivashinsky equation arising in the modeling of nanoscale ripple patterns that form when a nominally flat solid surface is bombarded with a broad ion…
We study convective stability of a two-front superposition in a reaction-diffusion system. Due to the instability of the connecting equilibrium, long-range semi-strong interaction is expected between the two waves. When restricting to the…
Two laboratory scale experiments of dry and under-water avalanches of non-cohesive granular materials are investigated. We trigger solitary waves and study the conditions under which the front is transversally stable. We show the existence…
The linearized water-wave radiation problem for an oscillating submerged line source in an inviscid shear flow with a free surface is investigated analytically at finite, constant depth in the presence of a shear flow varying linearly with…
We investigate the dynamics of a dilute suspension of hydrodynamically interacting motile or immotile stress-generating swimmers or particles as they invade a surrounding viscous fluid. Colonies of aligned pusher particles are shown to…
In this work we explore how nonlinear modes described by a dispersive wave equation (in our example, the nonlinear Schrodinger equation) and localized in a few wells of a periodic potential can act analogously to a chain of coupled…
We derive transport equations for the propagation of water wave action in the presence of a static, spatially random surface drift. Using the Wigner distribution $\W(\x,\k,t)$ to represent the envelope of the wave amplitude at position $\x$…
Charge, spin, as well as lattice instabilities are investigated in isolated or weakly coupled chains of correlated electrons at quarter-filling. Our analysis is based on extended Hubbard models including nearest neighbor repulsion and…
Here we study the nature and characteristics of waves propagating in partially ionised plasmas in the weakly ionised limit, typical for the lower part of the solar atmosphere. The framework in which the properties of waves are discussed…
The quantum dynamics of two weakly coupled nonlinear oscillators is analytically and numerically investigated in the context of nonlinear dissipation. The latter facilitates the creation and preservation of non-classical steady states.…
When waves impinge on a disordered material they are back-scattered and form a highly complex interference pattern. Suppressing any such distortions in the free propagation of a wave is a challenging task with many applications in a number…
The nonlinear aspects of longitudinal motion of interacting point masses in a lattice are revisited, with emphasis on the paradigm of charged dust grains in a dusty plasma (DP) crystal. Different types of localized excitations, predicted by…
The transmission lines we consider are constructed from the nonlinear inductors and the nonlinear capacitors. In the first part of the paper we additionally include linear ohmic resistors. Thus, the dissipation being taken into account…
Experimental results of towing a cylinder through a dense suspension of cornstarch and sucrose-water are presented. Focus is placed on the jamming fronts that exist in such systems. The literature has concentrated on the propagation of the…
We study the global well-posedness and asymptotic behavior for a semilinear damped wave equation with Neumann boundary conditions, modelling a one-dimensional linearly elastic body interacting with a rigid substrate through an adhesive…
In discrete nonlinear systems, the study of nonlinear waves has revealed intriguing phenomena in various fields such as nonlinear optics, biophysics, and condensed matter physics. Discrete nonlinear Schr\"odinger (DNLS) equations are often…
In the present paper we study phase waves of self-sustained oscillators with a nearest neighbor dispersive coupling on an infinite lattice. To analyze the underlying dynamics we approximate the lattice with a quasi-continuum, QC. The…
In a strongly nonlinear viscous granular chain under conditions of loading that exclude stationary waves (e.g., impact by a single grain) we observe a pulse that consists of two interconnected but distinct parts. One is a leading narrow…
This paper addresses the amplitude and phase dynamics of a large system non-linear coupled, non-identical damped harmonic oscillators, which is based on recent research in coupled oscillation in optomechanics. Our goal is to investigate the…
We study dispersion properties of linear surface gravity waves propagating in an arbitrary direction atop a current profile of depth-varying magnitude using a piecewise linear approximation, and develop a robust numerical framework for…