On the Existence of Quasipattern Solutions of the Swift–Hohenberg Equation
作者： G. Iooss , A. M. Rucklidge
DOI: 10.1007/S00332-010-9063-0
关键词: Quasiperiodic function 、 Quasiperiodicity 、 Partial differential equation 、 Mathematics 、 Swift–Hohenberg equation 、 Order (group theory) 、 Divisor (algebraic geometry) 、 Mathematical analysis 、 Divergent series 、 Pattern formation
摘要: Quasipatterns (two-dimensional patterns that are quasiperiodic in any spatial direction) remain one of the outstanding problems pattern formation. As with involving quasiperiodicity, there is a small divisor problem. In this paper, we consider 8-fold, 10-fold, 12-fold, and higher order quasipattern solutions Swift-Hohenberg equation. We prove formal solution, given by divergent series, may be used to build smooth function which an approximate solution pattern-forming partial differential equation (PDE) up exponentially error.
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