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 …

In this work, we provide two complementary perspectives for the (spectral) stability of solitary
traveling waves in Hamiltonian nonlinear dynamical lattices, of which the Fermi-Pasta-Ulam …

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 …

In the present work, we consider the existence and spectral stability of multi-pulse solutions
in Hamiltonian lattice systems which are invariant under a one-parameter unitary group of …

We explore the possibility of multi‐site breather states in a nonlinear Klein–Gordon lattice to
become nonlinearly unstable, even if they are found to be spectrally stable. The mechanism …

We consider the existence and spectral stability of static multi-kink structures in the discrete
sine-Gordon equation, as a representative example of the family of discrete Klein–Gordon …

We consider a one-dimensional discrete nonlinear Schrödinger (dNLS) model featuring
interactions beyond nearest neighbors. We are interested in the existence (or nonexistence) …

In the present chapter, we explore the possibility of a Frenkel-Kontorova (discrete sine-
Gordon) model to bear interactions that decay algebraically with space, inspired by the …

It is well known that one-dimensional Klein–Gordon lattices with nearest-neighbor
interactions can support multibreathers with phase differences between the successive …