  We consider the free boundary problem for a plasma--vacuum interface in ideal
incompressible magnetohydrodynamics. Unlike the classical statement, where the
vacuum magnetic field obeys the div-curl system of pre-Maxwell dynamics, we do
not neglect the displacement current in the vacuum region and consider the
Maxwell equations for electric and magnetic fields. Our aim is to construct
highly oscillating surface wave solutions in weakly nonlinear regime to this
plasma--vacuum interface problem.
  Under a necessary and sufficient stability condition for a piecewise constant
background state, we construct approximate solutions at any arbitrarily large
order of accuracy to the free boundary problem in three space dimensions when
the initial discontinuity displays high frequency oscillations. Moreover, such
approximate surface waves have nontrivial residual non-oscillatory components.
