A note on solution of the dispersion equation for small-amplitude internal waves

Abstract

This note is concerned with establishing the nature of the roots of a dispersion equation, which arises in the study of small-amplitude internal waves in two immiscible superposed fluids, wherein the upper fluid has a free surface and the lower fluid has a rigid bottom. All roots of this dispersion equation are found by considering graphs of appropriate functions, and the fact that these are the only possible roots, has been established by Rouche's theorem of complex variable theory.