  By integrating the full Maxwell's equations we predict the existence of gap
solitons in a quadratic, Fabry-Perot negative index cavity. An intense,
fundamental pump pulse shifts the band structure that forms when magnetic and
electric plasma frequencies are different so that a weak, second harmonic pulse
initially tuned inside the gap is almost entirely transmitted. The process is
due cascading, which occurs far from phase matching conditions, and causes
pulse compression. A nonlinear polarization spawns a dark soliton, while a
nonlinear magnetization produces a bright soliton.
