On the internal nonlinear resonance of capillary-gravitational waves on the charged surface of a deep viscous liquid

An analytical expression for the profile of a periodic wave of finite amplitude on the surface of a deep viscous conducting liquid is obtained for the first time. The formula admits the transition to a limiting case of the ideal liquid. It is shown that the position of an internal nonlinear resonance of these capillary-gravitational waves depends neither on the medium viscosity nor on the surface charging. It is established that, during the resonance interaction, the energy is pumped from longwave capillary-gravitational oscillations with the wavenumber k(*) equivalent to rootrhog/2gamma to shortwave oscillations with k(0) equivalent to root2rhog/gamma. (C) 2003 MAIK "Nauka / Interperiodica".