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

In a recent feature article in this journal, coauthored by Gert van der Heijden, I described the
static-dynamic analogy and its role in understanding the localized post-buckling of shell-like …

Biological functions in living systems are closely related to their geometries and
morphologies. Toroidal structures, which widely exist in nature, present interesting features …

The Swift-Hohenberg equation with quadratic and cubic nonlinearities exhibits a remarkable
wealth of stable spatially localized states. The presence of these states is related to a …

The study of spatial patterns in extended systems, and their evolution with time, poses
challenging questions for physicists and mathematicians alike. Waves on water, pulses in …

This paper considers an unfolding of a degenerate reversible 1–1 resonance (or
Hamiltonian–Hopf) bifurcation for four-dimensional systems of time reversible ordinary …

We study a partial integro-differential equation defined on a spatially extended domain that
arises from the modeling of" working" or short-term memory in a neuronal network. The …

The bistable Swift-Hohenberg equation exhibits multiple stable and unstable spatially
localized states of arbitrary length in the vicinity of the Maxwell point between spatially …

Honeycomb structures have a wide range of applications, from medical implants to industrial
components. In addition, honeycombs play a critical role when passive protection is required …

The elastic buckling of shell structures such as spherical shells subject to external pressure
and cylindrical shells loaded in axial compression is highly sensitive to imperfections and …