Related papers: Traveling waves in nonclassical diffusion equation…
This paper focuses on traveling wave solutions for the so-called Rosenzweig-MacArthur model with spatial diffusion. The main results of this note are concerned with the existence and uniqueness of traveling wave solution as well as periodic…
We consider a family of singular Volterra integral equations that appear in the study of monotone travelling-wave solutions for a family of diffusion-convection-reaction equations involving the $p$-Laplacian operator. Our results extend the…
A nonlocal derivative NLS (nonlinear Schr\"{o}dinger) equation describes modulations of waves in a stratified fluid and a continuous limit of the Calogero--Moser--Sutherland system of particles. For the defocusing version of this equation,…
We present experimental results on hydrothermal traveling-waves dynamics in long and narrow 1D channels. The onset of primary traveling-wave patterns is briefly presented for different fluid heights and for annular or bounded channels,…
We study an integro-differential equation that describes the slow erosion of granular flow. The equation is a first order non-linear conservation law where the flux function includes an integral term. We show that there exist unique…
We consider a free boundary model of epithelial cell migration with logistic growth and nonlinear diffusion induced by mechanical interactions. Using numerical simulations, phase plane and perturbation analysis, we find and analyse…
We prove the existence of a family of travelling wave solutions in a variant of the $\textit{Zeldovich-Frank-Kamenetskii (ZFK) equation}$, a reaction-diffusion equation which models the propagation of planar laminar premixed flames in…
We consider the existence of periodic traveling waves in a bidirectional Whitham equation, combining the full two-way dispersion relation from the incompressible Euler equations with a canonical shallow water nonlinearity. Of particular…
This paper deals with the existence, monotonicity, uniqueness and asymptotic behaviour of travelling wavefronts for a class of temporally delayed, spatially nonlocal diffusion equations.
Whitham modulation theory describes the zero dispersion limit of nonlinear waves by a system of conservation laws for the parameters of modulated periodic traveling waves. Here, admissible, discontinuous, weak solutions of the Whitham…
The famous Fisher-KPP reaction-diffusion model combines linear diffusion with the typical KPP reaction term, and appears in a number of relevant applications in biology and chemistry. It is remarkable as a mathematical model since it…
We consider reaction-diffusion equations on the planar square lattice that admit spectrally stable planar travelling wave solutions. We show that these solutions can be continued into a branch of travelling corners. As an example, we…
We describe traveling waves in a basic model for three-dimensional water-wave dynamics in the weakly nonlinear long-wave regime. Small solutions that are periodic in the direction of translation (or orthogonal to it) form an…
The Fisher-KPP equation with general nonlinear diffusion and arbitrary kinetic orders in the reaction terms is considered. The existence of oscillatory travelling wave solutions is proved for this model. Conditions for the existence of such…
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 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…
Proposed in this paper is a numerical procedure to generate periodic traveling wave solutions of some nonlinear dispersive wave equations. The method is based on a suitable modification of a fixed point algorithm of Petviahvili type and…
This paper is concerned with traveling wave solutions for a chemotaxis model with degenerate diffusion of porous medium type. We establish the existence of semi-finite traveling waves, including the sharp type and $C^1$ type semi-finite…
We consider a one-dimensional reaction-diffusion equation of Fisher-Kolmogoroff-Petrovsky-Piscounoff type. We investigate the effect of the interaction between the nonlinear diffusion coefficient and the reaction term on the existence and…
We study a reaction-diffusion-convection problem with nonlinear drift posed in a domain with periodically arranged obstacles. The non-linearity in the drift is linked to the hydrodynamic limit of a totally asymmetric simple exclusion…