Nonlinear capillary-gravity waves under an edge condition

The objective of this paper is to investigate the forced motion of nonlinear capillary-gravity waves in a waterfilled circular basin by a harmonic vibration applied to its side wall under Evans's or Hocking's edge condition at a contact line. The forcing frequency is near a resonance frequency under the classical edge condition of the basin. Two complex-amplitude equations for the excited eigenmode at the resonance frequency corresponding to these two edge conditions are derived. The solutions to these equations display quite different behavior and an edge condition indeed has a great influence on the excited surface waves.