  The polysymplectic analysis of the Short Pulse Equation known in nonlinear
optics is used in order to construct a geometric polysymplectic integrator for
it. The proposed scheme turns out to be much more effective than other standard
integration schemes for nonlinear PDEs, such as the pseudo-spectral integrator.
In our numerical experiments the polysymplectic integrator appears to be an
order of magnitude more precise and approximately 2.5 times faster at long
propagation times than the pseudo-spectral method.
