  In this paper we study the propagation of weakly nonlinear surface waves on a
plasma-vacuum interface. In the plasma region we consider the equations of
incompressible magnetohydrodynamics, while in vacuum the magnetic and electric
fields are governed by the Maxwell equations. A surface wave propagate along
the plasma-vacuum interface, when it is linearly weakly stable.
  Following the approach of Ali and Hunter, we measure the amplitude of the
surface wave by the normalized displacement of the interface in a reference
frame moving with the linearized phase velocity of the wave, and obtain that it
satisfies an asymptotic nonlocal, Hamiltonian evolution equation. We show the
local-in-time existence of smooth solutions to the Cauchy problem for the
amplitude equation in noncanonical variables, and we derive a blow up
criterion.
