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

DOI10.1016/j.physd.2005.03.009zbMath1125.82318arXivnlin/0403040OpenAlexW1982422860MaRDI QIDQ556369

D. S. Ryabov, K. G. Zhukov, G. M. Chechin

Publication date: 13 June 2005

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0403040

zbMATH Keywords

Nonlinear dynamicsanharmonic latticesDiscrete symmetryNormal mode interactions

Mathematics Subject Classification ID

Statistical mechanics of crystals (82D25) Complex behavior and chaotic systems of ordinary differential equations (34C28) Classical dynamic and nonequilibrium statistical mechanics (general) (82C05) Lattice dynamics; integrable lattice equations (37K60)

Related Items (14)

DISCRETE SYMMETRY AND STABILITY IN HAMILTONIAN DYNAMICS ⋮ The zone boundary mode in periodic nonlinear electrical lattices ⋮ Near-integrability and recurrence in FPU chains with alternating masses ⋮ Interaction of Lower and Higher Order Hamiltonian Resonances ⋮ Soliton solutions of generalized \((3+1)\)-dimensional Yu-Toda-Sasa-Fukuyama equation using Lie symmetry analysis ⋮ Delocalized nonlinear vibrational modes in Ni\(_3\)Al ⋮ Periodic orbits in nonlinear wave equations on networks ⋮ Exact solutions of nonlinear dynamical equations for large-amplitude atomic vibrations in arbitrary monoatomic chains with fixed ends ⋮ Dynamics of Oscillator Chains ⋮ Low-dimensional \(q\)-tori in FPU lattices: dynamics and localization properties ⋮ Delocalized nonlinear vibrational modes in fcc metals ⋮ Effect of discrete breathers on the specific heat of a nonlinear chain ⋮ Tail resonances of Fermi-Pasta-Ulam q-breathers and their impact on the pathway to equipartition ⋮ Impact of solitons on the progression of initial lesion in aortic dissection

Uses Software

• ISOTROPY

Cites Work

• Unnamed Item
• Computers and group-theoretical methods for studying structural phase transitions
• Stability of nonlinear modes and chaotic properties of 1D Fermi-Pasta-Ulam lattices
• Existence and stability of bushes of vibrational modes for octahedral mechanical systems with Lennard-Jones potential
• Exact solutions in the FPU oscillator chain
• Bushes of vibrational modes for Fermi-Pasta-Ulam chains
• Nonlinear normal modes for systems with discrete symmetry
• Symmetric invariant manifolds in the Fermi-Pasta-Ulam lattice
• Tangent bifurcation of band edge plane waves, dynamical symmetry breaking and vibrational localization
• Interactions between normal modes in nonlinear dynamical systems with discrete symmetry. Exact results
• The Normal Modes of Nonlinear n-Degree-of-Freedom Systems
• The anti-FPU problem

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