Self-trapping of light beams and parametric solitons in diffractive quadratic media

It is shown that the mutual trapping of the fundamental and second-harmonic beams in a diffractive (or dispersive) medium with quadratic nonlinearity can support a family of two-wave (2+1)-dimensional solitons of circular symmetry. The stability analysis shows that these (2+1)-dimensional solitons are stable in the physically important region of parameters, although unstable solitons are also revealed and their instability dynamics is analyzed numerically. Phase-dependent and, in some cases, nondestructive collisions of these solitons are also considered.