Global bifurcation theory of deep-water waves with vorticity

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The classical deep-water wave problem is to find a periodic traveling wave with a free surface of infinite depth. The main result is the construction of a global connected set of rotational solutions for a general class of vorticities. Each nontrivial solution on the continuum has a wave profile symmetric around the crests and monotone between crest and trough. The problem is formulated as a nonlinear elliptic boundary value problem in an unbounded domain with a parameter. The analysis is based on generalized degree theory and the global theory of bifurcation. The unboundedness of the domain renders consideration of approximate problems with stronger compactness properties.

Original languageEnglish (US)
Pages (from-to)1482-1521
Number of pages40
JournalSIAM Journal on Mathematical Analysis
Issue number5
StatePublished - Jan 2006
Externally publishedYes


  • Bifurcation
  • Leray-Schauder degree
  • Nonlinear elliptic
  • Vorticity
  • Water waves

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics


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