On the existence of quasipattern solutions of the Swift-Hohenberg equation

DOI10.1007/s00332-010-9063-0zbMath1195.35041arXiv0910.5350OpenAlexW1981123810WikidataQ58422052 ScholiaQ58422052MaRDI QIDQ989650

Alastair M. Rucklidge, Gérard Iooss

Publication date: 23 August 2010

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.5350

zbMATH Keywords

small divisorsGevrey seriesquasipatternexponentially small error

Mathematics Subject Classification ID

Asymptotic expansions of solutions to PDEs (35C20) Bifurcations in context of PDEs (35B32) Abel, Borel and power series methods (40G10) Quasicrystals and aperiodic tilings in discrete geometry (52C23) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55) Semilinear parabolic equations (35K58) Pattern formations in context of PDEs (35B36)

Related Items (13)

Spatiotemporal chaos and quasipatterns in coupled reaction-diffusion systems ⋮ Approximate localised dihedral patterns near a turing instability ⋮ Pattern formation for the Swift-Hohenberg equation on the hyperbolic plane ⋮ Small divisor problems in fluid mechanics ⋮ Multi-hump solutions with small oscillations at infinity for stationary Swift–Hohenberg equation ⋮ Existence of quasipattern solutions of the Swift-Hohenberg equation ⋮ Existence of bifurcating quasipatterns in steady Bénard-Rayleigh convection ⋮ Quasipatterns in a parametrically forced horizontal fluid film ⋮ On parametric Gevrey asymptotics for some Cauchy problems in quasiperiodic function spaces ⋮ Proof of quasipatterns for the Swift-Hohenberg equation ⋮ Periodic solutions and homoclinic solutions for a Swift-Hohenberg equation with dispersion ⋮ Existence of quasipatterns in the superposition of two hexagonal patterns ⋮ Patterns and Quasipatterns from the Superposition of Two Hexagonal Lattices

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