We find exact one-parameter families of stationary two-dimensional light bullets in the form of solitons localized in space and time in diffractive and dispersive nonlinear media under conditions for second-harmonic generation. We study the shape and various features of the solitons, including their stability during propagation, with emphasis on the general case of unequal group-velocity dispersions for the fundamental and second-harmonic waves when the transverse spatio-temporal shape of the solitons is asymmetric. It is shown that, when propagating in two-dimensional geometries, most of the spatio-temporal solitons are dynamically stable. q 1998 Elsevier Science B.V. All rights reserved

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