Nonlinear classical Hamiltonian lattices exhibit generic solutions—discrete breathers. They
are time-periodic and (typically exponentially) localized in space. The lattices have discrete …

The study of granular crystals, which are nonlinear metamaterials that consist of closely
packed arrays of particles that interact elastically, is a vibrant area of research that combines …

In the present work, we attempt a brief summary of various areas where non-linear waves
have been emerging in the phenomenology of lattice dynamical systems. These areas …

In this article we perform a thorough analysis of breathers in a one-dimensional model for a
layered silicate for which there exists fossil and experimental evidence of moving excitations …

Using the method of asymptotics beyond all orders, we evaluate the amplitude of radiation
from a moving small-amplitude soliton in the discrete nonlinear Schrödinger equation. When …

We present a particular type of one-dimensional nonlinear lattice that supports smoothly
propagating discrete breathers. The lattice is constructed by imposing a particular symmetry …

We present a study of the existence, stability, and bifurcation structure of families of dark
breathers in a one-dimensional uniform chain of spherical beads under static load. A …

We have studied moving discrete breathers in the Fermi–Pasta–Ulam β lattice. The moving
discrete breathers are not strictly localized but have spatially extended tails. It is shown that …

A well-known feature of a propagating localized excitation in a discrete lattice is the
generation of a backwave in the extended normal mode spectrum. To quantify the parameter …

The present work examines in detail the existence, stability and dynamics of travelling
solitary waves in a Schrödinger lattice with saturable nonlinearity. After analysing the linear …