Walking solitons in type II second-harmonic generation

We find the families of spatial walking solitons propagating in quadratic nonlinear media under conditions for type II second-harmonic generation in the presence of Poynting vector walk-off between the interacting beams. The analytical stability criterion for these three-parameter vector solitons is established. We study the shape and general properties of the solitons and their stability on propagation. It is found that the stationary solutions are stable at moderate positive phase mismatch. At phase matching and negative phase mismatch there are some unstable solutions near the cutoff.