Defect-mediated snaking: A new growth mechanism for localized structures

Yi-Ping Ma, J. Burke, Edgar Knobloch

Research output: Contribution to journalArticlepeer-review

52 Citations (Scopus)

Abstract

Stationary spatially localized patterns in parametrically driven systems are studied, focusing on the 2:1 and 1:1 resonance tongues as described by the forced complex Ginzburg–Landau equation. Homoclinic snaking is identified in both cases and the nature of the growth of the localized structures along the snaking branches is described. The structures grow from a central defect that inserts new rolls on either side, while pushing existing rolls outwards. This growth mechanism differs fundamentally from that found in other systems exhibiting homoclinic snaking in which new rolls are added at the fronts that connect the structure to the background homogeneous state.
Original languageEnglish
Pages (from-to)1867-1883
JournalPhysica D: Nonlinear Phenomena
Volume239
Issue number19
DOIs
Publication statusPublished - 1 Oct 2010

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