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

This book aims to provide an introduction to dynamical systems with multiple time scales. As
in any overview book, several topics are covered only quite briefly. My aim was to focus on …

Ecosystem regime shifts are regarded as abrupt global transitions from one stable state to
an alternative stable state, induced by slow environmental changes or by global …

In this paper, the approximated analytical solution for the fractional Swift–Hohenberg (S–H)
equation has been investigated with the help of the residual power series method (RPSM) …

The conserved Swift-Hohenberg equation with cubic nonlinearity provides the simplest
microscopic description of the thermodynamic transition from a fluid state to a crystalline …

In this paper, the approximated analytical solution for fractional Swift‐Hohenberg (S‐H)
equation is found with the aid of novel technique called q‐homotopy analysis transform …

In this study, the direct meshless local Petrov–Galerkin (DMLPG) method has been
employed to solve the stochastic Cahn–Hilliard–Cook and Swift–Hohenberg equations. First …

In this work, we study the bifurcation structures and the stability of multidimensional localized
states within coherently driven Kerr optical cavities with parabolic potentials in 1D, 2D, and …

Localized coherent structures can form in externally driven dispersive optical cavities with a
Kerr-type non-linearity. Such systems are described by the Lugiato–Lefever (LL) equation …

We study localized activity patterns in neural field equations posed on the Euclidean plane;
such models are commonly used to describe the coarse-grained activity of large ensembles …