Small planar travelling waves in two-dimensional networks of coupled oscillators

Research output: Contribution to journalArticle

1 Citation (Scopus)
65 Downloads (Pure)

Abstract

The existence of several small planar travelling waves with arbitrary direction of propagation is shown for two-dimensional cubic networks of oscillators with linear nearest-neighbour coupling. The analysis is based on a spatial dynamics reformulation of the relevant advance-delay equation. Whereas important aspects of the analysis are discontinuous in the direction of travel, and continuity of the travelling wave is shown with respect to the direction.
Original languageEnglish
Pages (from-to)157-170
Number of pages14
JournalDynamical Systems: An International Journal
Volume24
Issue number2
DOIs
Publication statusPublished - 2009

Fingerprint

Coupled Oscillators
Traveling Wave
Delay Equations
Reformulation
Nearest Neighbor
Propagation
Arbitrary

Keywords

  • breathers
  • pasta-ulam lattice
  • nonlinear oscillators
  • normal forms
  • centre manifold theory
  • solitary waves
  • discrete
  • chain
  • travelling waves
  • advance-delay equation
  • lattice dynamics
  • infinite-dimensional Hamiltonian dynamics
  • fpu lattices

Cite this

Small planar travelling waves in two-dimensional networks of coupled oscillators. / Pfrang, C; Matthies, Karsten.

In: Dynamical Systems: An International Journal, Vol. 24, No. 2, 2009, p. 157-170.

Research output: Contribution to journalArticle

@article{e8c771b5bb6d476f9014ab25297dfd6f,
title = "Small planar travelling waves in two-dimensional networks of coupled oscillators",
abstract = "The existence of several small planar travelling waves with arbitrary direction of propagation is shown for two-dimensional cubic networks of oscillators with linear nearest-neighbour coupling. The analysis is based on a spatial dynamics reformulation of the relevant advance-delay equation. Whereas important aspects of the analysis are discontinuous in the direction of travel, and continuity of the travelling wave is shown with respect to the direction.",
keywords = "breathers, pasta-ulam lattice, nonlinear oscillators, normal forms, centre manifold theory, solitary waves, discrete, chain, travelling waves, advance-delay equation, lattice dynamics, infinite-dimensional Hamiltonian dynamics, fpu lattices",
author = "C Pfrang and Karsten Matthies",
year = "2009",
doi = "10.1080/14689360802541281",
language = "English",
volume = "24",
pages = "157--170",
journal = "Dynamical Systems: An International Journal",
issn = "1468-9367",
publisher = "Taylor and Francis",
number = "2",

}

TY - JOUR

T1 - Small planar travelling waves in two-dimensional networks of coupled oscillators

AU - Pfrang, C

AU - Matthies, Karsten

PY - 2009

Y1 - 2009

N2 - The existence of several small planar travelling waves with arbitrary direction of propagation is shown for two-dimensional cubic networks of oscillators with linear nearest-neighbour coupling. The analysis is based on a spatial dynamics reformulation of the relevant advance-delay equation. Whereas important aspects of the analysis are discontinuous in the direction of travel, and continuity of the travelling wave is shown with respect to the direction.

AB - The existence of several small planar travelling waves with arbitrary direction of propagation is shown for two-dimensional cubic networks of oscillators with linear nearest-neighbour coupling. The analysis is based on a spatial dynamics reformulation of the relevant advance-delay equation. Whereas important aspects of the analysis are discontinuous in the direction of travel, and continuity of the travelling wave is shown with respect to the direction.

KW - breathers

KW - pasta-ulam lattice

KW - nonlinear oscillators

KW - normal forms

KW - centre manifold theory

KW - solitary waves

KW - discrete

KW - chain

KW - travelling waves

KW - advance-delay equation

KW - lattice dynamics

KW - infinite-dimensional Hamiltonian dynamics

KW - fpu lattices

UR - http://www.scopus.com/inward/record.url?scp=70349510629&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1080/14689360802541281

U2 - 10.1080/14689360802541281

DO - 10.1080/14689360802541281

M3 - Article

VL - 24

SP - 157

EP - 170

JO - Dynamical Systems: An International Journal

JF - Dynamical Systems: An International Journal

SN - 1468-9367

IS - 2

ER -