On Composite Steady-State Capillary-Gravitational Finite Amplitude Waves.

Steady-state finite-amplitude waves caused by pressure periodically distributed along the surface of a liquid and disappearing when this pressure becomes constant, are termed 'forced' steady-state finite amplitude waves corresponding to constant pressure at the surface values of flow velocity are termed 'free'. The possibility of simultaneous existence of both types of capillary-gravitational waves of small but finite amplitude at special values of flow velocity at an infinite depth is established. These waves are termed composite. When the variable part of the pressure distributed over the surface turns identically to zero, these waves do not disappear but become free. The problem is strictly formulated and is reduced to the solution of a system of three nonlinear equations, one of which is integral and the other two are transcendental. An approximate equation of the wave profile is given.