Related papers: Theoretical / numerical study of modulated traveli…
{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…
When the steady states at infinity become unstable through a pattern forming bifurcation, a travelling wave may bifurcate into a modulated front which is time-periodic in a moving frame. This scenario has been studied by B.Sandstede and…
Motivated by earlier studies of artificial perceptions of light called phosphenes, we analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model…
In this work, we study a model of a one-dimensional magnetic metamaterial formed by a discrete array of nonlinear resonators. We focus on periodic and localized traveling waves of the model, in the presence of loss and an external drive.…
The present paper is concerned with the existence of traveling wave solutions of the asymptotic model, derived by the authors in a previous work, to approximate the unidirectional evolution of a collision-free plasma in a magnetic field.…
In this paper, we investigate the existence, uniqueness, and spectral stability of traveling waves arising from a single threshold neural field model with one spatial dimension, a Heaviside firing rate function, axonal propagation delay,…
We consider a one-dimensional Swift-Hohenberg equation coupled to a conservation law, where both equations contain additional dispersive terms breaking the reflection symmetry $x \mapsto -x$. This system exhibits a Turing instability and we…
The purpose of this work is to introduce a concept of traveling waves in the setting of periodic metric graphs. It is known that the nonlinear Schr{\"o}dinger (NLS) equation on periodic metric graphs can be reduced asymptotically on long…
In this paper we consider the spectral and nonlinear stability of periodic traveling wave solutions of a generalized Kuramoto-Sivashinsky equation. In particular, we resolve the long-standing question of nonlinear modulational stability by…
Traveling modulating pulse solutions consist of a small amplitude pulse-like envelope moving with a constant speed and modulating a harmonic carrier wave. Such solutions can be approximated by solitons of an effective nonlinear Schrodinger…
In the dynamics generated by the suspension bridge equation, traveling waves are an essential feature. The existing literature focuses primarily on the idealized one-dimensional case, while traveling structures in two spatial dimensions…
In this paper, we study the traveling wave solutions to the density-suppressed motility model describing the ``self-trapping'' mechanism that induces spatio-temporal pattern formations observed in the experiment. We establish the existence…
Neural field equations offer a continuous description of the dynamics of large populations of synaptically coupled neurons. This makes them a convenient tool to describe various neural processes, such as working memory, motion perception,…
The theory of traveling waves and spreading speeds is developed for time-space periodic monotone semiflows with monostable structure. By using traveling waves of the associated Poincar\'e maps in a strong sense, we establish the existence…
In this paper, we investigate the modulational stability of periodic traveling waves in a local model for shallow water waves, which is an extended version of the Hunter-Saxton equation. We construct a family of small-amplitude periodic…
We consider a nonlocal generalization of the Fisher-KPP equation in one spatial dimension. As a parameter is varied the system undergoes a Turing bifurcation. We study the dynamics near this Turing bifurcation. Our results are two-fold.…
We study the effects of additive noise on traveling pulse solutions in spatially extended neural fields with linear adaptation. Neural fields are evolution equations with an integral term characterizing synaptic interactions between neurons…
We study travelling wave solutions of a 1D continuum model for collective cell migration in which cells are characterised by position and polarity. Four different types of travelling wave solutions are identified which represent…
The traveling wave with the peaked profile arises in the limit of the family of traveling waves with the smooth profiles. We study the linear and nonlinear stability of the peaked traveling wave by using a local model for shallow water…
We investigate the instabilities and bifurcations of traveling pulses in a model excitable medium; in particular we discuss three different scenarios for the loss of stability resp. the disappearance of stable pulses. In numerical…