Walking light bullets

Two-parameter families of chirped stationary two-dimensional light bullets, in the form of localized spatio-temporal solitons in dispersive-diffractive quadratically nonlinear optical media under conditions for the Type I second-harmonic generation, are constructed in the presence of the temporal walkoff. One of the two parameters is the velocity of the soliton's walk relative to its carrier waves. Basic features of the walking light bullets, including a comprehensive consideration of their dynamical stability, are studied in the general case of unequal group-velocity dispersions at the fundamental and second-harmonic frequencies. The transverse shapes of the walking light bullets exhibit a spatio-temporal asymmetry. It is concluded that, when propagated in two-dimensional geometries, most of the two-dimensional walking light bullets are dynamically stable, hence they may be observed in an experiment.