NONLINEAR INTERNAL RESONANCE IN CAPILLARY-GRAVITY WAVES

The method of multiple scales is used to study the second harmonic resonance of weakly nonlinear progressive capillary-gravity waves on a conducting fluid in the presence of a magnetic field. The dynamical equations governing the amplitudes of interacting waves are obtained. We investigate the spatial behaviour of the amplitudes and phases. It is shown that the motion is bounded for all distances. In the steady state, it is observed that the general motion consists of both amplitude and phase modulated waves.