### Abstract

Behavior of a periodic travelling wave-train is studied. 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.

Original language | English |
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Pages (from-to) | 469-485 |

Number of pages | 17 |

Journal | Proc R Soc London Ser A |

Volume | 363 |

Issue number | 1715 |

Publication status | Published - 1 Jan 1978 |

### ASJC Scopus subject areas

- Mathematics(all)
- Engineering(all)
- Physics and Astronomy(all)

## Cite this

Toland, J. F. (1978). ON THE EXISTENCE OF A WAVE OF GREATEST HEIGHT AND STOKE'S CONJECTURE.

*Proc R Soc London Ser A*,*363*(1715), 469-485.