Bushes of vibrational modes for Fermi-Pasta-Ulam chains

Details Bushes of vibrational modes for Fermi-Pasta-Ulam chains Bushes of vibrational modes for Fermi-Pasta-Ulam chains

2002-01-26

arxiv.org/abs/nlin/0201050v2

Nonlinear Sciences

Chaotic Dynamics

To be published in Physica D

Scientific paper

10.1016/S0167-2789(02)00430-X

Some exact solutions and multi-mode invariant submanifolds were found for the Fermi-Pasta-Ulam (FPU) beta-model by Poggi and Ruffo in Phys. D 103 (1997) 251. In the present paper we demonstrate how results of such a type can be obtained for an arbitrary N-particle chain with periodic boundary conditions with the aid of our group-theoretical approach [Phys. D 117 (1998) 43] based on the concept of bushes of normal modes for mechanical systems with discrete symmetry. The integro-differential equation describing the FPU-alfa dynamics in the modal space is derived. The loss of stability of the bushes of modes for the FPU-alfa model, in particular, for the limiting case N >> 1 for the dynamical regime with displacement pattern having period twice the lattice spacing (Pi-mode) is studied. Our results for the FPU-alfa chain are compared with those by Poggi and Ruffo for the FPU-beta chain.

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