Abstract The cubic complex Ginzburg-Landau equation is one of the most-studied nonlinear
equations in the physics community. It describes a vast variety of phenomena from nonlinear …

This paper is an introductory review of the problem of front propagation into unstable states.
Our presentation is centered around the concept of the asymptotic linear spreading velocity …

▪ Abstract The objective of this review is to critically assess the different approaches
developed in recent years to understand the dynamics of open flows such as mixing layers …

Pattern formation in physical systems is one of the major research frontiers of mathematics.
A central theme of this book is that many instances of pattern formation can be understood …

Spatial localization is a common feature of physical systems, occurring in both conservative
and dissipative systems. This article reviews the theoretical foundations of our …

Instabilities of nonlinear waves on unbounded domains manifest themselves in different
ways. An absolute instability occurs if the amplitude of localized wave packets grows in time …

Although the origin of Earth's and other celestial bodies' magnetic fields remains unknown,
we do know that the motion of electrically conducting fluids generates and maintains these …

Recent advances in mean-field theory are reviewed and applications to the Sun, late-type
stars, accretion disks, galaxies and the early Universe are discussed. We focus particularly …

A family of slowly spatially develo** wakes with variable pressure gradient is numerically
demonstrated to sustain a synchronized finite-amplitude vortex street tuned at a well-defined …

Numerical continuation is used to compute solution branches in a two-component reaction-
diffusion model of Leslie–Gower type. Two regimes are studied in detail. In the first, the …