The propagation of a fundamental wave and the frequency-doubled wave, in media with cascaded second order optical nonlinearities, is calculated from the equations:
Gaussian solutions are:
We have shown that:
Stationary solutions (gaussian solitons) belong to a one-parameter family whose wavefront is plane and the Q"1 parameter is the real root of the following cubic polynomial:
Starting from initial conditions slightly different of the ones leading to solitons, we find that the solitons due to cascaded second order nonlinearities exhibit some stability:
