Presidential Address 1968: Initial value problems in two-dimensional water wave theory.

Abstract

As it is the custom for the retiring President to devote the last hour, or so, of his term of office in addressing the assembled members and visitors on a topic which is of special interest to him, I would like to attempt, in the time available, a brief survey of one aspect of what is known in Fluid Dynamics as Surface Waves. An idea of the breadth of the topic Surface Waves can be illustrated by referring to the excellent and comprehensive survey of Wehausen and Laitone [16], which occupies some 300 pages. Obviously, then, it is possible only to attempt a description of one small aspect of this field, and the aspect I have chosen is Initial Value Problems in Two-Dimensional Water Wave Theory.When turning through the pages of the early volumes of the Society's Journal, I was pleased to see that the first paper published was mathematical. The paper [2], by the Honourable Chief Justice Cockle, F.R.S., President of the Queensland Philosophical Society, was on "' Non-linear Coresolvents '', and was read to the Society on 7th August, 1867, by Martin Gardiner, Esq., C.E. I was convinced that, due to the Society's long association with Mathematics, I should endeavour to present a mathematical topic as the basis of this address. However, I became somewhat apprehensive on reading further and finding the following remark made by the Rev. W. B. Clarke [1] at the end of the reading of Cockle's paper: '"' The learned mathematical treatise by the Chief Justice of Queensland, although beyond the appreciation of many, does honour. . ."'. However, despite the apprehension, my conviction persisted.