Equation of steady-state capillary gravitational-gyroscopic waves on shallow water and Kelvin waves

On the basis of a spectral asymptotic method developed by the authors, a rigorous derivation is given on the equation of capillary waves on shallow water with consideration of the rotation of the fluid and its stratification. The character of the wave motions described by this equation is investigated, and the existence of capillary Kelvin waves is established. Moreover, the problem of the diffraction of these waves by a half plane is studied.Translated from Itogi Nauki i Tekhniki, Seriya Matematicheskii Analiz, Vol. 24, pp. 207–268, 1986.