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.