Finite-amplitude solitary water waves

C. J. Amick, J. F. Toland

Research output: Contribution to journalArticlepeer-review


This paper considers the existence problem for solutions of the free boundary value problem which arises from the question of the existence of solitary gravity waves without changes of form, and with constant velocity, on the surface of ideal fluid in a horizontal canal of finite depth. The analysis imposes no restriction on either the slope or the amplitude of the wave, and we prove that there exists a connected set of solitary waves containing waves of all slope between 0 and PI/6. It is then proved that each of these solitary waves has finite mass, and, as a consequence, that F1, where F is the Froude number. Finally, it is shown that, in a certain limit, these solitary waves converge to a solitary stokes wave of greatest height, and the validty of Stokes, conjecture for solitary waves is considered, but not resolved. (A)

Original languageEnglish
Issue numberMRC-TSR-2012)
Publication statusPublished - 1 Jan 1979

ASJC Scopus subject areas

  • Engineering(all)


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