Related papers: Two classes of nonlocal Evolution Equations relate…
We discuss the application of a variant of the method of simplest equation for obtaining exact traveling wave solutions of a class of nonlinear partial differential equations containing polynomial nonlinearities. As simplest equation we use…
We consider a wide class of model equations, able to describe wave propagation in dispersive nonlinear media. The Korteweg-de Vries (KdV) equation is derived in this general frame under some conditions, the physical meanings of which are…
This study deals with the analysis of the Cauchy problem of a general class of nonlocal nonlinear equations modeling the bi-directional propagation of dispersive waves in various contexts. The nonlocal nature of the problem is reflected by…
In this paper, we characterized an analytical and numerical study of the resonant interaction between waves in MHD. A system of evolution equations is derived; we focus on the study of the interaction between a selected triad. The resulting…
The work presented here emanates from questions arising from experimental observations of the propagation of surface water waves. The experiments in question featured a periodically moving wavemaker located at one end of a flume that…
We study the traveling wave solutions to a reaction diffusion system modeling the public goods game with altruistic behaviors. The existence of the waves is derived through monotone iteration of a pair of classical upper- and lower…
We consider an infinite-sized population where an infinite number of traits compete simultaneously. The replicator equation with a diffusive term describes time evolution of the probability distribution over the traits due to selection and…
It is universally accepted that the cubic, nonlinear Schrodinger equation (NLS) models the dynamics of narrow-bandwidth wave packets consisting of short dispersive waves, while the Kortewegde Vries equation (KdV) models the propagation of…
In this paper we will establish nonlinear a priori lower and upper bounds for the solutions to a large class of equations which arise from the study of traveling wave solutions of reaction-diffusion equations, and we will apply our…
In linear science, the wave motion equation with general D'Alembert wave solutions is one of the fundamental models. The D'Alembert wave is an arbitrary travelling wave moving along one direction under a fixed model (material) dependent…
We consider quasi-stationary (travelling wave type) solutions to a nonlinear reaction-diffusion equation with arbitrary, autonomous coefficients, describing the evolution of glioblastomas, aggressive primary brain tumors that are…
We study a nonlocal reaction-diffusion-mutation equation modeling the spreading of a cane toads population structured by a phenotypical trait responsible for the spatial diffusion rate. When the trait space is bounded, the cane toads…
The classical wave equation in the space of generalized functions (distributions)is considered. The Distributions Method of building the solutions of nonstationary boundary value problems (NBVP) for wave equations in coordinates spaces of…
We consider the nonlocal KPP-Fisher equation $u_t(t,x) = u_{xx}(t,x) + u(t,x)(1-(K *u)(t,x))$ which describes the evolution of population density $u(t,x)$ with respect to time $t$ and location $x$. The non-locality is expressed in terms of…
We investigate the connection between the existence of an explicit travelling wave solution and the travelling wave with minimal speed in a scalar monostable reaction-diffusion equation.
In a companion paper, we established nonlinear stability with detailed diffusive rates of decay of spectrally stable periodic traveling-wave solutions of reaction diffusion systems under small perturbations consisting of a nonlocalized…
In this paper, we study the orbital stability for a four-parameter family of periodic stationary traveling wave solutions to the generalized Korteweg-de Vries equation. In particular, we derive sufficient conditions for such a solution to…
Numerical simulations of the unidirectional random waves are performed within the Korteweg -de Vries equation to investigate the statistical properties of surface gravity waves in shallow water. Nonlinear evolution shows the relaxation of…
This paper is devoted to the investigation of spatial spreading speeds and traveling wave solutions of monostable evolution equations with nonlocal dispersal in time and space periodic habitats. It has been shown in an earlier work by the…
A one species time-delay reaction-diffusion system defined on a complex networks is studied. Travelling waves are predicted to occur as follows a symmetry breaking instability of an homogenous stationary stable solution, subject to an…