Nonlinear resonance interaction between three capillary-gravity waves on the plane charged fluid surface

Three-wave interaction between capillary-gravity waves on a uniformly charged free fluid surface is analyzed using second-order analytic calculations. The time evolution of the wave amplitudes in the state of nonlinear resonance is studied. It is shown that the number of three-wave resonances is infinite and their exact locations for waves of finite amplitude depend on the initial conditions.