Solitary waves in a finite depth fluid

Abstract

It is shown that U( xi )=u₀(cosh² a xi +(ab)^-2 sinh² a xi )^-1 is the exact stationary wave solution to the Whitham equation in a two-layer fluid of finite depth and represents the natural connection between the Benjamin-Ono deep water (a to 0) and Kortweg-de Vries shallow water (b to infinity ) theories.