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Multi-pulse evolution and space-time chaos in dissipative systems

About this Title

Sergey Zelik and Alexander Mielke

Publication: Memoirs of the American Mathematical Society
Publication Year: 2009; Volume 198, Number 925
ISBNs: 978-0-8218-4264-5 (print); 978-1-4704-0531-1 (online)
DOI: https://doi.org/10.1090/memo/0925
MathSciNet review: 2499464
MSC: Primary 35Q53; Secondary 35B41, 37L10, 37L30

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Table of Contents

Chapters

  • 1. Introduction
  • 2. Assumptions and preliminaries
  • 3. Weighted Sobolev spaces and regularity of solutions
  • 4. The multi-pulse manifold: General structure
  • 5. The multi-pulse manifold: Projectors and tangent spaces
  • 6. The multi-pulse manifold: Differential equations and the cut off procedure
  • 7. Slow evolution of multi-pulse profiles: Linear case
  • 8. Slow evolution of multi-pulse structures: Center manifold reduction
  • 9. Hyperbolicity and stability
  • 10. Multi-pulse evolution equations: Asymptotic expansions
  • 11. An application: Spatio-temporal chaos in periodically perturbed Swift-Hohenberg equation