Solitary Waves in the One- and Two-Fluid Systems

Abstract

A theoretical discussion is given of the solitary wave. Part I is concerned with the wave on a water surface; Part II considers the solitary wave at the interface of two superimposed liquids of different density, bounded above and below by rigid surfaces. In Part I higher approximations are obtained for the speed of propagation, and limits to the wave speed are derived from the momentum theorem. The results include a correction to the second approximation of Weinstein. In Part II the first two approximations to the wave speed are derived. The equations of the second approximation yield limits on the wave amplitude.