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Title: |
Interfaces between rolls in the Swift-Hohenberg equation |
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Author: |
Mariana Haragus, Arnd Scheel 
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Address: |
Laboratoire de Mathematiques, Universite de Franche-Comte, 16 route de Gray, 25030 Besancon cedex, France. ' School of Mathematics, University of Minnesota, 206 Church St. S.E., Minneapolis, MN 55455, USA |
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Journal: |
International Journal of Dynamical Systems and Differential Equations 2007 - Vol. 1, No.2 pp. 89 - 97 |
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Abstract: |
We study the existence of interfaces between stripe or roll solutions in the Swift-Hohenberg equation. We prove the existence of two different types of interfaces: corner-like interfaces, also referred to as knee solutions, and step-like interfaces. The analysis relies upon a spatial dynamics formulation of the existence problem and an equivariant centre-manifold reduction. In this setting, the interfaces are found as heteroclinic and homoclinic orbits of a reduced system of ODEs. |
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Keywords: |
interfaces; roll solutions; stripe solutions; spatial dynamics; Swift-Hohenberg equation; zigzag instability; centre manifold reduction; ODEs; ordinary differential equations. |
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DOI: |
10.1504/IJDSDE.2007.016510 |
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