Stability of nonlinear modes and chaotic properties of 1D Fermi-Pasta-Ulam lattices

Nurit Budinsky, Tassos Bountis

Research output: Contribution to journalArticle

53 Citations (Scopus)

Abstract

The stability properties of certain simple periodic solutions (nonlinear modes) of the equations of motion of one-dimensional, N-particle FPU lattices, are obtained analytically by uncoupling the N linear variational equations. The energy per particle Ec/N at which these modes first become unstable is calculated and its asymptotic behavior as N→∞ is determined. We find that for lattices which experience strong energy sharing Ec/N →0 as N →∞, while for a lattice where little energy sharing is observed Ec/N →const > 0, as N increases. Certain possible connections between our local stability results and some global chaotic properties of FPU lattices are discussed.

Original languageEnglish
Pages (from-to)445-452
Number of pages8
JournalPhysica D: Nonlinear Phenomena
Volume8
Issue number3
DOIs
Publication statusPublished - 1983
Externally publishedYes

Fingerprint

Equations of motion
Sharing
Energy
Variational Equation
Local Stability
energy
Equations of Motion
Linear equation
Periodic Solution
equations of motion
Asymptotic Behavior
Unstable
Experience

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

Stability of nonlinear modes and chaotic properties of 1D Fermi-Pasta-Ulam lattices. / Budinsky, Nurit; Bountis, Tassos.

In: Physica D: Nonlinear Phenomena, Vol. 8, No. 3, 1983, p. 445-452.

Research output: Contribution to journalArticle

Budinsky, Nurit ; Bountis, Tassos. / Stability of nonlinear modes and chaotic properties of 1D Fermi-Pasta-Ulam lattices. In: Physica D: Nonlinear Phenomena. 1983 ; Vol. 8, No. 3. pp. 445-452.
@article{6a2907530c6b48e6bd57c95ddadadd0a,
title = "Stability of nonlinear modes and chaotic properties of 1D Fermi-Pasta-Ulam lattices",
abstract = "The stability properties of certain simple periodic solutions (nonlinear modes) of the equations of motion of one-dimensional, N-particle FPU lattices, are obtained analytically by uncoupling the N linear variational equations. The energy per particle Ec/N at which these modes first become unstable is calculated and its asymptotic behavior as N→∞ is determined. We find that for lattices which experience strong energy sharing Ec/N →0 as N →∞, while for a lattice where little energy sharing is observed Ec/N →const > 0, as N increases. Certain possible connections between our local stability results and some global chaotic properties of FPU lattices are discussed.",
author = "Nurit Budinsky and Tassos Bountis",
year = "1983",
doi = "10.1016/0167-2789(83)90236-1",
language = "English",
volume = "8",
pages = "445--452",
journal = "Physica D: Nonlinear Phenomena",
issn = "0167-2789",
publisher = "Elsevier",
number = "3",

}

TY - JOUR

T1 - Stability of nonlinear modes and chaotic properties of 1D Fermi-Pasta-Ulam lattices

AU - Budinsky, Nurit

AU - Bountis, Tassos

PY - 1983

Y1 - 1983

N2 - The stability properties of certain simple periodic solutions (nonlinear modes) of the equations of motion of one-dimensional, N-particle FPU lattices, are obtained analytically by uncoupling the N linear variational equations. The energy per particle Ec/N at which these modes first become unstable is calculated and its asymptotic behavior as N→∞ is determined. We find that for lattices which experience strong energy sharing Ec/N →0 as N →∞, while for a lattice where little energy sharing is observed Ec/N →const > 0, as N increases. Certain possible connections between our local stability results and some global chaotic properties of FPU lattices are discussed.

AB - The stability properties of certain simple periodic solutions (nonlinear modes) of the equations of motion of one-dimensional, N-particle FPU lattices, are obtained analytically by uncoupling the N linear variational equations. The energy per particle Ec/N at which these modes first become unstable is calculated and its asymptotic behavior as N→∞ is determined. We find that for lattices which experience strong energy sharing Ec/N →0 as N →∞, while for a lattice where little energy sharing is observed Ec/N →const > 0, as N increases. Certain possible connections between our local stability results and some global chaotic properties of FPU lattices are discussed.

UR - http://www.scopus.com/inward/record.url?scp=48749142942&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=48749142942&partnerID=8YFLogxK

U2 - 10.1016/0167-2789(83)90236-1

DO - 10.1016/0167-2789(83)90236-1

M3 - Article

VL - 8

SP - 445

EP - 452

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 3

ER -