INTEGRABILITY AND LOCALIZED EXCITATIONS IN NONLINEAR DISCRETE-SYSTEMS

We analyze the origin and features of localized excitations in nonline ar discrete Klein-Gordon systems. We convect the presence of stationar y excitations with the existence of local integrability of the origina l N-degree-of-freedom system. The method consists of constructing a re duced problem of a few degrees of freedom and analyzing its phase-spac e structure with the help of geometrical methods (Poincare maps). We f ind a correspondence between regular and chaotic motion in the reduced problem on one side and localized and delocalized states in the infin ite system on the other side. The periodic trajectories corresponding to elliptic fixed points of the Poincare map are related to previous n umerical and analytical studies. We analyze the stability of the perio dic orbits with respect to small-amplitude phonons as well as the inte rnal stability of multiple-frequency localized excitations. We find an energy threshold for the existence of stationary localized excitation s and an energy threshold for the existence of instabilities due to in ternal resonances (onset of chaos). Approximation schemes accounting f or the main properties of stationary localized excitations are applied .