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

Bushes of normal modes represent the exact excitations in the nonlinear physical systems with discrete symmetries [Physica D 117 (1998) 43]. The present paper is the continuation of our previous paper [Physica D 166 (2002) 208], where these dynamical objects of 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- and two-dimensional vibrational bushes for both FPU- α and FPU- β models, in particular, of those revealed recently in [Physica D 175 (2003) 31].