Bushes of vibrational modes for Fermi-Pasta-Ulam chains

DOI10.1016/S0167-2789(02)00430-XzbMath1094.82505arXivnlin/0201050MaRDI QIDQ1599054

N. V. Novikova, A. A. Abramenko, G. M. Chechin

Publication date: 4 June 2002

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

Full work available at URL: https://arxiv.org/abs/nlin/0201050

zbMATH Keywords

periodic boundary conditionsintegro-differential equationmultimode invariant submanifolds

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)

Related Items (18)

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 ⋮ Periodic travelling waves of forced FPU lattices ⋮ Interaction of Lower and Higher Order Hamiltonian Resonances ⋮ THEORY OF TRANSPORT PROCESSES AND THE METHOD OF THE NONEQUILIBRIUM STATISTICAL OPERATOR ⋮ Soliton solutions of generalized \((3+1)\)-dimensional Yu-Toda-Sasa-Fukuyama equation using Lie symmetry analysis ⋮ Exact solutions of nonlinear dynamical equations for large-amplitude atomic vibrations in arbitrary monoatomic chains with fixed ends ⋮ Dynamics of Oscillator Chains ⋮ Measures of chaos and equipartition in integrable and nonintegrable lattices ⋮ Fermi–Pasta–Ulam, solitons and the fabric of nonlinear and computational science: History, synergetics, and visiometrics ⋮ The anti-FPU problem ⋮ Stability of low-dimensional bushes of vibrational modes in the Fermi-Pasta-Ulam chains ⋮ Isochronism and tangent bifurcation of band edge modes in Hamiltonian lattices ⋮ Exceptional Discretizations of the NLS: Exact Solutions and Conservation Laws ⋮ Two novel methods and multi-mode periodic solutions for the Fermi-Pasta-Ulam model ⋮ Symmetric invariant manifolds in the Fermi-Pasta-Ulam lattice ⋮ 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
• Existence and stability of bushes of vibrational modes for octahedral mechanical systems with Lennard-Jones potential
• Exact solutions in the FPU oscillator chain
• Nonlinear normal modes for systems with discrete symmetry
• 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
• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
• Stability of nonlinear normal modes of symmetric Hamiltonian systems
• Existence of nonlinear normal modes of symmetric Hamiltonian systems

This page was built for publication: Bushes of vibrational modes for Fermi-Pasta-Ulam chains