One-dimensional chains are used as a fundamental model of condensed matter, and have
constituted the starting point for key developments in nonlinear physics and complex …

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 …

Small-amplitude weakly coupled oscillators of the Klein–Gordon lattices are approximated
by equations of the discrete nonlinear Schrödinger type. We show how to justify this …

Discrete breathers are ubiquitous structures in nonlinear anharmonic models ranging from
the prototypical example of the Fermi-Pasta-Ulam model to Klein-Gordon nonlinear lattices …

We prove a general criterion of spectral stability of multi-site breathers in the discrete Klein–
Gordon equation with a small coupling constant. In the anti-continuum limit, multi-site …

Localized excitations have been at the heart of developments of nonlinear dynamics (and
especially of nonlinear complex systems) during the past few decades. Their names may …

We consider discrete breathers in one-dimensional diatomic Fermi–Pasta–Ulam type
lattices. A discrete breather in the limit of zero mass ratio, ie the anti-continuous limit …

We study the existence and stability of multibreathers in Klein–Gordon chains with
interactions that are not restricted to nearest neighbors. We provide a general framework …

Deflation is an efficient numerical technique for identifying new branches of steady state
solutions to nonlinear partial differential equations. Here, we demonstrate how to extend …

The problem of showing the existence of localized modes in nonlinear lattices has attracted
considerable efforts not only from the physical but also from the mathematical viewpoint …