Rigorous numerics for localized patterns to the quintic swift-hohenberg equation

Yasuaki Hiraoka, Toshiyuki Ogawa

研究成果: Article

11 引用 (Scopus)

抜粋

Localized patterns of the quintic Swift-Hohenberg equation are studied by bifurcation analysis and rigorous numerics. First of all, fundamental bifurcation structures around the trivial solution are investigated by a weak nonlinear analysis based on the center manifold theory. Then bifurcation structures with large amplitude are studied on Galerkin approximated dynamical systems, and a relationship between snaky branch structures of saddle-node bifurcations and localized patterns is discussed. Finally, a topological numerical verification technique proves the existence of several localized patterns as an original infinite dimensional problem, which are beyond the local analysis.

元の言語English
ページ(範囲)57-75
ページ数19
ジャーナルJapan Journal of Industrial and Applied Mathematics
22
発行部数1
DOI
出版物ステータスPublished - 2005 2

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

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