Proposed resolution of theory-experiment discrepancy in homoclinic snaking

W.J. Firth, L. Columbo, A. Scroggie

Research output: Contribution to journalArticle

50 Citations (Scopus)

Abstract

In spatially extended Turing-unstable systems, parameter variation should, in theory, produce only fully developed patterns. In experiment, however, localized patterns or solitons sitting on a smooth background often appear. Addition of a nonlocal nonlinearity can resolve this discrepancy by tilting the "snaking" bifurcation diagram characteristic of such problems.

LanguageEnglish
Pages104503
Number of pages4
JournalPhysical Review Letters
Volume99
Issue number10
DOIs
Publication statusPublished - 7 Sep 2007

Fingerprint

lateral oscillation
solitary waves
diagrams
nonlinearity

Keywords

  • pattern selection
  • pattern formation
  • optics
  • solitons
  • bifurcation
  • physics

Cite this

Firth, W.J. ; Columbo, L. ; Scroggie, A. / Proposed resolution of theory-experiment discrepancy in homoclinic snaking. In: Physical Review Letters. 2007 ; Vol. 99, No. 10. pp. 104503.
@article{ce9c102fbc7b430eb5fa9386b8783cc6,
title = "Proposed resolution of theory-experiment discrepancy in homoclinic snaking",
abstract = "In spatially extended Turing-unstable systems, parameter variation should, in theory, produce only fully developed patterns. In experiment, however, localized patterns or solitons sitting on a smooth background often appear. Addition of a nonlocal nonlinearity can resolve this discrepancy by tilting the {"}snaking{"} bifurcation diagram characteristic of such problems.",
keywords = "pattern selection, pattern formation, optics, solitons, bifurcation, physics",
author = "W.J. Firth and L. Columbo and A. Scroggie",
year = "2007",
month = "9",
day = "7",
doi = "10.1103/PhysRevLett.99.104503",
language = "English",
volume = "99",
pages = "104503",
journal = "Physical Review Letters",
issn = "0031-9007",
number = "10",

}

Proposed resolution of theory-experiment discrepancy in homoclinic snaking. / Firth, W.J.; Columbo, L.; Scroggie, A.

In: Physical Review Letters, Vol. 99, No. 10, 07.09.2007, p. 104503.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Proposed resolution of theory-experiment discrepancy in homoclinic snaking

AU - Firth, W.J.

AU - Columbo, L.

AU - Scroggie, A.

PY - 2007/9/7

Y1 - 2007/9/7

N2 - In spatially extended Turing-unstable systems, parameter variation should, in theory, produce only fully developed patterns. In experiment, however, localized patterns or solitons sitting on a smooth background often appear. Addition of a nonlocal nonlinearity can resolve this discrepancy by tilting the "snaking" bifurcation diagram characteristic of such problems.

AB - In spatially extended Turing-unstable systems, parameter variation should, in theory, produce only fully developed patterns. In experiment, however, localized patterns or solitons sitting on a smooth background often appear. Addition of a nonlocal nonlinearity can resolve this discrepancy by tilting the "snaking" bifurcation diagram characteristic of such problems.

KW - pattern selection

KW - pattern formation

KW - optics

KW - solitons

KW - bifurcation

KW - physics

U2 - 10.1103/PhysRevLett.99.104503

DO - 10.1103/PhysRevLett.99.104503

M3 - Article

VL - 99

SP - 104503

JO - Physical Review Letters

T2 - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 10

ER -