The aim of this review article is to present recent advances in the theory of the dynamics of
modulated phases in the Frenkel-Kontorova model. This theory is motivated through two …

Controllable switching between metastable macroscopic quantum states under
nonequilibrium conditions induced either by light or with an external electric field is rapidly …

Greene (1979) proposed a relationship between the existence of an invariant circle for an
area-preserving map and the'residues' of periodic orbits with nearby rotation number. It …

We study travelling waves on a two-dimensional lattice with linear and nonlinear coupling
between nearest particles and a periodic nonlinear substrate potential. Such a discrete …

We consider existence and stability properties of nonlinear spatially periodic or
quasiperiodic standing waves (SWs) in one-dimensional lattices of coupled anharmonic …

A rigorous proof for the existence of bipolaronic states is given for the adiabatic Holstein
model for any lattice at any dimension, periodic or not, and for an arbitrary band filling …

There is a well-known correspondence between the dynamics of symplectic twist maps
which represent an important class of Hamiltonian systems and the equilibrium states of a …

Many models for structures in condensed matter can be associated with Hamiltonian
dynamical systems with discrete time. This connection is due to the fact that both models are …

We study the transmission coefficient of a plane wave through a one-dimensional finite
quasiperiodic system—the Frenkel-Kontorova (FK) model—embedding in an infinite uniform …

We study the existence and branching patterns of wave trains in a two-dimensional lattice
with linear and nonlinear coupling between nearest particles and a nonlinear substrate …