Numerical solution of nonlinear wave equations in stratified dispersive media

Nonlinear wave motion in dispersive media is solved numerically. The model applies to laser propagation in a relativistic plasma. The latter causes, besides dispersion, nonlinear effects due to relativistic mass variation in the presence of strong laser pulses. A new variant of the Gautschi-type integrator for reducing the number of time steps is proposed as a fast solver for such nonlinear wave-equations. In order to reduce the number of spatial grid points, a physically motivated quasi-envelope approach (QEA) is introduced. The new method turns out to reduce the computational time significantly compared to the standard leap-frog scheme.