Skip to Main content Skip to Navigation
Journal articles

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

Abstract : 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.
Complete list of metadata

Cited literature [31 references]  Display  Hide  Download
Contributor : Gerard Iooss <>
Submitted on : Sunday, January 31, 2016 - 10:19:19 AM
Last modification on : Monday, October 12, 2020 - 2:28:05 PM
Long-term archiving on: : Friday, November 11, 2016 - 10:38:24 PM


Files produced by the author(s)



Gérard Iooss, Alastair Rucklidge. On the Existence of Quasipattern Solutions of the Swift–Hohenberg Equation. Journal of Nonlinear Science, Springer Verlag, 2010, ⟨10.1007/s00332-010-9063-0⟩. ⟨hal-01265174⟩



Record views


Files downloads