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].

References in corpus (4)

• Bushes of vibrational modes for Fermi-Pasta-Ulam chains
• The Anti-FPU Problem
• Symmetric invariant manifolds in the Fermi-Pasta-Ulam lattice
• Numerical analysis of the one-mode solutions in the Fermi-Pasta-Ulam system

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• Studying of nonlinear normal modes interactions in SF6 molecule with the aid of the density functional theory
• Discrete Symmetry and Stability in Hamiltonian Dynamics
• Modulational instability in isolated and driven Fermi--Pasta--Ulam lattices
• Low-dimensional q-Tori in FPU Lattices: Dynamics and Localization Properties
• Thermostatistics in the neighborhood of the $\pi$-mode solution for the Fermi-Pasta-Ulam $\beta$ system: from weak to strong chaos
• Stability of Nonlinear Normal Modes in the FPU-$\beta$ Chain in the Thermodynamic Limit
• Stable and unstable periodic orbits in the one dimensional lattice ${\varphi }^4$ theory
• Periodic orbits in nonlinear wave equations on networks
• Explorations for alternating FPU-chains with large mass
• Delocalized periodic vibrations in nonlinear electrical chains
• Properties of large-amplitudes vibrations in dynamical systems with discrete symmetry. Geometrical aspects