Light bullets in a planar waveguide with quadratic nonlinearity and normal group velocity dispersion

We study self-similar solutions to the second-harmonic-generation equations in a planar waveguide with transversal inhomogeneity of the refractive index, taking into account the mutual influence of quadratic nonlinearity, second-order diffraction and weak linear dispersion. Both parabolic profile and profile with saturation are investigated. It is demonstrated that waveguide geometry plays the fundamental role for spatio-temporal solitons (light bullets) existence provided that the normal dispersion is at both frequencies.