In the last decade, non-linear dynamical transport in semiconductor superlattices (SLs) has
witnessed significant progress in theoretical descriptions as well as in experimentally …

We obtain existence of traveling wave solutions for a class of spatially discrete systems,
namely, lattice differential equations. Uniqueness of the wave speed c, and uniqueness of …

Nonlinear charge transport in semiconductor superlattices under strong electric fields
parallel to the growth direction results in rich dynamical behaviour including the formation of …

In this paper, we study a very general non-local lattice differential equation with delay. We
obtain the existence of the asymptotic speed of propagation, the existence and uniqueness …

We consider spatially discrete bistable reaction-diffusion equations that admit wave front
solutions. Depending on the parameters involved, such wave fronts appear to be pinned or …

We discuss recent results in the theory of lattice differential equations (LDE's), particularly for
LDE's of diffusive type. Broadly speaking, an LDE is an infinite system of ordinary differential …

Problems in engineering, computational science, and the physical and biological sciences
are using increasingly sophisticated mathematical techniques. Thus, the bridge between the …

Pinning and depinning of wave fronts are ubiquitous features of spatially discrete systems
describing a host of phenomena in physics, biology, etc. A large class of discrete systems is …

We study a Lotka–Volterra type competition system with bistable nonlinearity in which the
habitat is divided into discrete niches. We show that there exist non-monotone stationary …

Propagation of pulses in myelinated fibers may be described by appropriate solutions of
spatially discrete FitzHugh--Nagumo systems. In these systems, propagation failure may …