Related papers: Existence of traveling wave solutions for a nonloc…
We analyze the conditions, which guarantee the existence of periodic and soliton-like traveling wave solutions in the non-local hydrodynamic model of structured media.
This paper deals with front propagation dynamics of monostable equations with nonlocal dispersal in spatially periodic habitats. In the authors' earlier works, it is shown that a general spatially periodic monostable equation with nonlocal…
This paper is concerned with the existence and the stability of travelling wave solutions to a bistable reaction-diffusion equation with a jump discontinuious point on nonlinear term. Sub-super solution method is used throughout this paper.…
We consider an evolution equation of parabolic type in R having a travelling wave solution. We perform an appropriate change of variables which transforms the equation into a non local evolution one having a travelling wave solution with…
We study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the Euler equations for inviscid, incompressible and homogenous fluids. We obtain solitary waves of…
In this article we are concerned with the existence and orbital stability of traveling wave solutions of a general class of nonlocal wave equations: $ u_{tt}-Lu_{xx}=B(\pm |u|^{p-1}u)_{xx}$, $ p>1$. The main characteristic of this class of…
We prove the existence and uniqueness, for wave speeds sufficiently large, of monotone traveling wave solutions connecting stable to unstable spatial equilibria for a class of $N$-dimensional lattice differential equations with…
We prove the existence of small amplitude time quasi-periodic solutions of the pure gravity water waves equations with constant vorticity, for a bidimensional fluid over a flat bottom delimited by a space periodic free interface. Using a…
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.…
Nonlinear fronts between spatially extended traveling wave convection (TW) and quiescent fluid and spatially localized traveling waves (LTWs) are investigated in quantitative detail in the bistable regime of binary fluid mixtures heated…
For a class of scalar partial differential equations that incorporate convection, diffusion, and possibly dispersion in one space and one time dimension, the stability of traveling wave solutions is investigated. If the initial perturbation…
This paper reports results on the classification of traveling wave solutions, including nonnegative weak sense, in the spatial 1D degenerate parabolic equation. These are obtained through dynamical systems theory and geometric approaches…
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…
The travelling wave problem for a particular bidirectional Whitham system modelling surface water waves is under consideration. This system firstly appeared in [Dinvay, Dutykh, Kalisch 2018], where it was numerically shown to be stable and…
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…
We consider a single component reaction-diffusion equation in one dimension with bistable nonlinearity and a nonlocal space-fractional diffusion operator of Riesz-Feller type. Our main result shows the existence, uniqueness (up to…
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 work we revisit a classical problem of traveling waves in a damped Frenkel-Kontorova lattice driven by a constant external force. We compute these solutions as fixed points of a nonlinear map and obtain the corresponding kinetic…
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…
This article produces wave equations and constructs traveling wave solutions that are intimately related to Newton's equations of celestial mechanics. The traveling wave solutions are expressed in ``closed form'' in terms of elementary…