On the existence of a wave of greatest height and Stokes’s conjecture

1978/11/27 by John Toland · 5 citations
Earth and Planetary Sciences · Mathematics · #Ocean Waves and Remote Sensing #Differential Equations and Numerical Methods #Aquatic and Environmental Studies #Conjecture #Mathematics #Conservative vector field #Limit (mathematics) #Limiting #Mathematical analysis #Flow (mathematics) #Wave equation #Pure mathematics #Geometry #Physics #Compressibility #Mechanics

paper · doi:10.1098/rspa.1978.0178

openalex publication_date 1978/11/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/05/21

Abstract

Abstract It is shown that there exists a solution of Nekrasov’s integral equation which corresponds to the existence of a wave of greatest height and of permanent form moving on the surface of an irrotational, infinitely deep flow. It is also shown that this wave is the uniform limit, in a specified sense, of waves of almost extreme form. The question of the validity of Stokes’s conjecture is reduced to one of the regularity of the solution of Nekrasov’s equation in this limiting case.

Citations

• The singularity at the crest of a finite amplitude progressive Stokes wave
• Computer extension and analytic continuation of Stokes’ expansion for gravity waves
• Steep gravity waves in water of arbitrary uniform depth
• The deformation of steep surface waves on water - I. A numerical method of computation
• D�termination rigoureuse des ondes permanentes d'ampleur finie

Cited by

• A Proof of the Stokes Conjecture in the Theory of Surface Waves*
• Superharmonic instability of stokes waves
• Branch Cuts of Stokes Wave on Deep Water. Part I: Numerical Solution and Padé Approximation
• Strongly Nonlinear Waves
• Stokes wave [wikipedia]