Slow passage through parametric resonance for a weakly nonlinear   dispersive wave
  A solution of the nonlinear Klein-Gordon equation perturbed by a parametric driver is studied. The frequency of the parametric perturbation varies slowly and passes through a resonant value. It yields a change in a solution. We obtain a connection formula for the asymptotic solution before and after the resonance. 
S. Glebov, O. Kiselev, N. Tarkhanov