Related papers: Tunable front interaction and localization of peri…
Localized traveling-wave pulses and holes, i.e. localized regions of vanishing wave amplitude, are investigated in a real Ginzburg-Landau equation coupled to a long-wave mode. In certain parameter regimes the pulses exhibit a Hopf…
We study cumulative scattering effects on wave front propagation in time dependent randomly layered media. It is well known that the wave front has a deterministic characterization in time independent media, aside from a small random shift…
In this paper, we present an asymptotic model describing localised flexural vibrations along a structured ring containing point masses or spring-mass resonators in an elastic plate. The values for the required masses and stiffnesses of…
We investigate the stability of stratified fluid layers undergoing homogeneous and periodic tidal deformation. We first introduce a local model which allows to study velocity and buoyancy fluctuations in a Lagrangian domain periodically…
The influence of extreme external forcing on traveling-wave dynamics in an ensemble of weakly nonlocally coupled excitable FitzHugh--Nagumo systems is studied. Three types of external exposure are considered: periodic Gaussian pulses,…
We explore the dynamics of non-interacting particles loaded into a phase-modulated one-dimensional lattice formed by laterally oscillating square barriers. Tuning the parameters of the driven unit cell of the lattice selected parts of the…
{We study a model of small-amplitude traveling waves arising in a supercritical Hopf-bifurcation, that are coupled to a slowly varying, real field. The field is advected by the waves and, in turn, affects their stability via a coupling to…
The localization of two interacting electrons in a coupled-quantum-dots semiconductor structure is demonstrated through numerical calculations of the time evolution of the two-electron wave function including the Coulomb interaction between…
The interacting vorticity wave formalism for shear flow instabilities is extended here to the magnetohydrodynamic (MHD) setting, to provide a mechanistic description for the stabilising and destabilising of shear instabilities by the…
The present work studies the influence of nonlocal spatial coupling on the existence of localized structures in 1-dimensional extended systems. We consider systems described by a real field with a nonlocal coupling that has a linear…
We consider the localization of elastic waves in thin elastic structures with spatially varying curvature profiles, using a curved rod and a singly curved shell as concrete examples. Previous studies on related problems have broadly focused…
We use Renormalization Group ideas to study stability of moving fronts in the Ginzburg-Landau equation in one spatial dimension. In particular, we prove stability of the real fronts under complex perturbations. This extends the results of…
The emergence of localised vibrations in cyclic and symmetric rotating structures, such as bladed disks of aircraft engines, has challenged engineers in the past few decades. In the linear regime, localised states may arise due to a lack of…
We introduce a new wave phenomenon, which can be observed in continuum and discrete systems, where a trapped mode exists under certain conditions, namely, the anti-localization of non-stationary linear waves. This is zeroing of the…
We study a system of interacting particles in a periodically moving external potential, within the simplest possible description of paradigmatic symmetric exclusion process on a ring. The model describes diffusion of hardcore particles…
The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schroedinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and…
We analyze the stability and dynamics of bistable planar fronts in multicomponent reaction-diffusion systems on $\mathbb{R}^{d}$. Under standard spectral stability assumptions, we establish Lyapunov stability of the front against fully…
This article introduces a physically realistic model for explaining how electromagnetic waves can be internally generated, propagate and interact in strongly magnetized plasmas or in nuclear magnetic resonance experiments. It studies high…
We establish nonlinear stability and asymptotic behavior of traveling periodic waves of viscous conservation laws under localized perturbations or nonlocalized perturbations asymptotic to constant shifts in phase, showing that long-time…
The dynamical phase transition of a system with two coexisting competing order parameters is studied using the time-dependent-Ginzburg-Landau framework. The dynamics are induced by parameters capturing the physics of driving the system with…