Proof of Quasipatterns for the Swift-Hohenberg Equation

Braaksma, B., Iooss, G. & Stolovitch, L. Jul-2017 In : Communications in Mathematical Physics. 353, 1, p. 37-67 31 p.

Research output: Scientific - peer-reviewArticle

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  • Proof of Quasipatterns for the Swift–Hohenberg Equation

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    Embargo ends: 01/07/2018

  • Proof of Quasipatterns for the Swift–Hohenberg Equation

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This paper establishes the existence of quasipatterns solutions of the Swift-Hohenberg PDE. In a former approach we avoided the use of Nash-Moser scheme, but our proof contains a gap. The present proof of existence is based on the works by Berti et al related to the Nash-Moser scheme. For solving the small divisor problem, we need to introduce a new free parameter related to the freedom in the choice of parameterization of the bifurcating solution. Thanks to a transversality condition, the result gives only a bifurcating set, located in a small hornlike region centered on a curve, with the origin at the bifurcation point.

Original languageEnglish
Pages (from-to)37-67
Number of pages31
JournalCommunications in Mathematical Physics
Issue number1
StatePublished - Jul-2017



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