Exact solitary water waves with vorticity

Research output: Contribution to journalArticlepeer-review


The solitary water wave problem is to find steady free surface waves which approach a constant level of depth in the far field. The main result is the existence of a family of exact solitary waves of small amplitude for an arbitrary vorticity. Each solution has a supercritical parameter value and decays exponentially at infinity. The proof is based on a generalized implicit function theorem of the Nash-Moser type. The first approximation to the surface profile is given by the "KdV" equation. With a supercritical value of the surface tension coefficient, a family of small amplitude solitary waves of depression with subcritical parameter values is constructed for an arbitrary vorticity.

Original languageEnglish (US)
Pages (from-to)213-244
Number of pages32
JournalArchive for Rational Mechanics and Analysis
Issue number2
StatePublished - May 2008
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering


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