  An error analysis of a splitting method applied to the Zakharov system is
given. The numerical method is a Lie-Trotter splitting in time that is combined
with a Fourier collocation in space to a fully discrete method. First-order
convergence in time and high-order convergence in space depending on the
regularity of the exact solution are shown for this method. The main challenge
in the analysis is to exclude a loss of spatial regularity in the numerical
solution. This is done by transforming the numerical method to new variables
and by imposing a natural CFL-type restriction on the discretization
parameters.
