Solitary internal waves in continuously stratified fluids of great depth

This paper considers the existence of solitary internal waves moving with a constant speed in a continuously stratified fluid of great depth. The fluid is inviscid, incompressible, and bounded below by a rigid bottom only. The density of fluid decreases continuously upwards to a certain level and then the fluid above has a constant density and extends to the infinity vertically. It is rigorously shown that the exact governing equations of this flow have a solitary wave solution that decays algebraically to a uniform state at infinity when the wave speed is near its first critical value. The first-order approximation of the solution is the solution obtained from the Benjamin–Ono equation (time independent).