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Bushes of vibrational modes for Fermi-Pasta-Ulam chains | | G. M. Chechin
; N. V. Novikova
; A. A. Abramenko
; | | Date: |
26 Dec 2001 | | Subject: | Chaotic Dynamics | nlin.CD | | Abstract: | 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. | | Source: | arXiv, nlin.CD/0201050 | | Services: | Forum | Review | PDF | Favorites | |
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