In this paper we study the propagation of weakly nonlinear surface waves on aplasma-vacuum interface. In the plasma region we consider the equations ofincompressible magnetohydrodynamics, while in vacuum the magnetic and electricfields are governed by the Maxwell equations. A surface wave propagate alongthe plasma-vacuum interface, when it is linearly weakly stable. Following the approach of Ali and Hunter, we measure the amplitude of thesurface wave by the normalized displacement of the interface in a referenceframe moving with the linearized phase velocity of the wave, and obtain that itsatisfies an asymptotic nonlocal, Hamiltonian evolution equation. We show thelocal-in-time existence of smooth solutions to the Cauchy problem for theamplitude equation in noncanonical variables, and we derive a blow upcriterion.
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