Stationary gravity waves with the zero mean vorticity in stratified fluid

A new approach to the description of stationary plane waves in ideal density stratified incompressible fluid is considered without the application of Boussinesq approximation. The approach is based on the equation derived by Dubreil-Jacotin and Long with the additional assumption that the mean vorticity of the flow is zero. It is shown that in the linear approximation the spectrum of eigenmodes and dispersion equations corresponding to these eigenmodes can be found in the closed analytical forms for many particular relationships between the fluid density and stream function. Examples are presented for waves of infinitesimal amplitude. Exact expression for the velocity of solitary wave of any amplitude is derived