Journal
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
Volume 23, Issue 1, Pages 93-114Publisher
SPRINGER
DOI: 10.1007/s10884-010-9195-9
Keywords
Homoclinic snaking; Isolas; Multi-pulses; Swift-Hohenberg equation
Categories
Funding
- London Mathematical Society
- Royal Society
- NSF [DMS-0907904]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0907904] Funding Source: National Science Foundation
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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.
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