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JNS
2010

On the Existence of Quasipattern Solutions of the Swift-Hohenberg Equation

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On the Existence of Quasipattern Solutions of the Swift-Hohenberg Equation
Quasipatterns (two-dimensional patterns that are quasiperiodic in any spatial direction) remain one of the outstanding problems of pattern formation. As with problems involving quasiperiodicity, there is a small divisor problem. In this paper, we consider 8-fold, 10-fold, 12-fold, and higher order quasipattern solutions of the Swift–Hohenberg equation. We prove that a formal solution, given by a divergent series, may be used to build a smooth quasiperiodic function which is an approximate solution of the pattern-forming PDE up to an exponentially small error.
G. Iooss, A. M. Rucklidge
Added 28 Jan 2011
Updated 28 Jan 2011
Type Journal
Year 2010
Where JNS
Authors G. Iooss, A. M. Rucklidge
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