On the theory of long waves

Abstract

A new method of studying plane steady wave motion of a gravity fluid is elucidated in this paper. This method succeeds in establishing the existence of a solitary wave, for example, and in giving the first complete foundation for the approximate Rayleigh theory [1], which concerns the theory of finite-amplitude long waves. Underlying the method are general boundary properties of univalent functions, used earlier by the author to construct a qualitative theory of jet fluid motions [2].