Related papers: Traveling waves for a lattice dynamical system ari…
In this paper we consider a scalar parabolic equation on a star graph; the model is quite general but what we have in mind is the description of traffic flows at a crossroad. In particular, we do not necessarily require the continuity of…
Dynamical systems containing heteroclinic cycles and networks can be invoked as models of intransitive competition between three or more species. When populations are assumed to be well-mixed, a system of ordinary differential equations…
We are concerned with the persistence of both predator and prey in a diffusive predator-prey system with a climate change effect, which is modeled by a spatial-temporal heterogeneity depending on a moving variable. Moreover, we consider…
We study waves in a chain of dispersively coupled phase oscillators. Two approaches -- a quasi-continuous approximation and an iterative numerical solution of the lattice equation -- allow us to characterize different types of traveling…
We perform the analysis of a hyperbolic model which is the analog of the Fisher-KPP equation. This model accounts for particles that move at maximal speed $\epsilon^{-1}$ ($\epsilon\textgreater{}0$), and proliferate according to a reaction…
This paper considers two-dimensional stratified water waves propagating under the force of gravity over an impermeable flat bed and with a free surface. We prove the existence of a global continuum of classical solutions that are periodic…
We study the asymptotic solutions of a version of the Balitsky-Kovchegov evolution with discrete steps in rapidity. We derive a closed iterative equation in momentum space. We show that it possesses traveling-wave solutions and extract…
Using a lattice string model, a number of peculiar excitation situations related to non-propagating excitations and non-radiating sources are demonstrated. External fields can be used to trap excitations locally but also lead to the ability…
Travelling waves of densities of binary fluid mixtures are investigated near a critical point. The free energy is considered in a non-local form taking account of the density gradients. The equations of motions are applied to a universal…
We study an asymmetric simple exclusion process in a strip in the presence of a solid impenetrable barrier. We focus on the effect of the barrier on the residence time of the particles, namely, the typical time needed by the particles to…
We consider a three-species predator-prey system involving two competing predators and one prey. The species diffuse with nonlocal dispersal kernels with possibly non-compact support, and they interact in a heterogeneous environment moving…
Analysis of mathematical models in ecology and epidemiology often focuses on asymptotic dynamics, such as stable equilibria and periodic orbits. However, many systems exhibit long transient behaviors where certain aspects of the dynamics…
e study the minimal wave speed and the asymptotics of the traveling wave solutions of a competitive Lotka Volterra system. The existence of the traveling wave solutions is derived by monotone iteration. The asymptotic behaviors of the wave…
The topic of this paper are nonlinear traveling waves occuring in a system of damped waves equations in one space variable. We extend the freezing method from first to second order equations in time. When applied to a Cauchy problem, this…
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…
Many physical, chemical and biological systems have an inherent discrete spatial structure that strongly influences their dynamical behaviour. Similar remarks apply to internal or external noise, as well as to nonlocal coupling. In this…
Nonreciprocal wave propagation allows for directional energy transport. In this work, we systematically investigate wave dynamics in an elastic lattice that combines nonreciprocal stiffness with viscous damping. After establishing how…
Existence of non-negative weak solutions is shown for a full curvature thin-film model of a liquid thin film flowing down a vertical fibre. The proof is based on the application of a priori estimates derived for energy-entropy functionals.…
We report experimental observations of traveling waves in a pure fluid with a free surface situated in a long container submitted to a horizontal temperature gradient perpendicular to its large extension. Above a critical value of the…
We study the wave solutions for a degenerated reaction diffusion system arising from the invasion of cells. We show that there exists a family of waves for the wave speed larger than or equals a certain number, and below which there is no…