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Isolas of 2-Pulse Solutions in Homoclinic Snaking Scenarios

  • Jürgen Knobloch
  • David J. B. Lloyd
  • Björn Sandstede
  • Thomas Wagenknecht
Article

Abstract

Homoclinic snaking refers to the bifurcation structure of symmetric localised roll patterns that are often found to lie on two sinusoidal “snaking” bifurcation curves, which are connected by an infinite number of “rung” segments along which asymmetric localised rolls of various widths exist. The envelopes of all these structures have a unique maximum and we refer to them as symmetric or asymmetric 1-pulses. In this paper, the existence of stationary 1D patterns of symmetric 2-pulses that consist of two well-separated 1-pulses is established. Corroborating earlier numerical evidence, it is shown that symmetric 2-pulses exist along isolas in parameter space that are formed by parts of the snaking curves and the rungs mentioned above.

Keywords

Homoclinic snaking Isolas Multi-pulses Swift–Hohenberg equation 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Jürgen Knobloch
    • 1
  • David J. B. Lloyd
    • 2
  • Björn Sandstede
    • 3
  • Thomas Wagenknecht
    • 4
  1. 1.Department of MathematicsTechnical University IlmenauIlmenauGermany
  2. 2.Department of MathematicsUniversity of SurreyGuildfordUK
  3. 3.Division of Applied MathematicsBrown UniversityProvidenceUSA
  4. 4.Department of Applied MathematicsUniversity of LeedsLeedsUK

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