Progressive waves of permanent form in continuously stratified fluids

A theory for internal progressive waves of permanent form in any continuously stratified fluid is presented, and a calculation for the flow and the wave velocity is carried out for an exponential stratified fluid. The most important conclusion from this calculation, also valid for other weak stratifications, is that the wave velocity always decreases with the amplitude, provided the density gradient is weak and the wavelength is not too short. This conclusion is significant because it entails the existence or nonexistence of solitary waves in weakly stratified fluids. The validity of the Boussinesq approximation and the significance of the well‐known exactly linear cases are also discussed.