ABSTRACT
The plane fluid flow problem with a free boundary has been investigated earlier. This chapter examines the planar problem associated with waves in incompressible, heavy fluids, specifically, the model suggested by Lavrent’ev and Shabat. It is assumed that the bottom of the reservoir is planar and the wave moves linearly with constant speed. The mobile coordinate system moving with the wave is chosen, with one axis passing through the maximum point of the wave and another axis pointing along the bottom in the direction of movement. The chapter presents a problem when complex speed is not equal to zero and Y is the maximum point of the wave. Such waves are called Stokes’s waves: they are peaked at the maximum.
