Nonlinear waves on the free surface of an electrically conducting liquid

Gravity waves of small but finite amplitude on the free surface of an electrically conducting liquid are examined. For the waves whose propagation is described by the Korteweg-de Vries equation (in the absence of a magnetic field), equations are derived. In addition to nonlinearity and dispersion, these equations include the influence of applied magnetic fields. As an example, the effect of magnetic damping on a solitary wave is presented.