  Several recently developed multisymplectic schemes for Hamiltonian PDEs have
been shown to preserve associated local conservation laws and constraints very
well in long time numerical simulations. Backward error analysis for PDEs, or
the method of modified equations, is a useful technique for studying the
qualitative behavior of a discretization and provides insight into the
preservation properties of the scheme. In this paper we initiate a backward
error analysis for PDE discretizations, in particular of multisymplectic box
schemes for the nonlinear Schrodinger equation. We show that the associated
modified differential equations are also multisymplectic and derive the
modified conservation laws which are satisfied to higher order by the numerical
solution. Higher order preservation of the modified local conservation laws is
verified numerically.
