Stability of low-dimensional bushes of vibrational modes in the Fermi-Pasta-Ulam chains

Abstract

Bushes of normal modes represent the exact excitations in nonlinear physical systems with discrete symmetries [Physica D117 (1998) 43]. The present paper is the continuation of our previous paper [Physica D166 (2002) 208], where these dynamical objects of a new type were discussed for the monoatomic nonlinear chains. Here, we develop a simple crystallographic method for finding bushes in nonlinear chains and investigate stability of one-dimensional and two-dimensional vibrational bushes for both FPU-alpha and FPU-beta models, in particular, of those revealed recently in [Physica D175 (2003) 31].