Abstract
A problem concering steary, capillary-gravitational waves of finite amplitude generated by pressure periodically distributed over the surface of an infinitely deep stream is considered. A rigorous solution of this problem is presented, with the surface pressure given, in the form of an infinite trigonometric series. In addition a particular case of investigated when the wavelength of the given pressure coincides with the length of the steady free wave corresponding to the specified flow velocity and constant pressure at the surface. The waves investigated here cease to exist when the periodic part of the pressure distributed over the surface vanishes identically and the flow becomes uniform. Such waves have been called induced [1]. An analogous problem for gravitational waves was investigated earlier [2] by the author. In addition, the author used the Levi-Civita method [3,4] to reduce a similar problem for free capillary-gravitational waves, to a nonlinear differential equation. In the present paper the problem is reduced to solbing a certain nonlinear integral equation. The latter is discussed and its solution is constructed for any degree of approximation. The first three approximations are derived completely and an approximate equation describing the wave profile is given.
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