Three-dimensional walking spatiotemporal solitons in quadratic media

Two-parameter families of chirped stationary three-dimensional spatiotempor al solitons in dispersive quadratically nonlinear optical media featuring t ype-I second-harmonic generation are constructed in the presence of tempora l walk-off. Basic features of these walking spatiotemporal solitons, includ ing their dynamical stability, are investigated in the general case of uneq ual group-velocity dispersions at the fundamental and second-harmonic frequ encies. In the cases when the solitons are unstable, the growth rate of a d ominant perturbation eigenmode is found as a function of the soliton wave n umber shift. The findings are in full agreement with the stability predicti ons made on the basis of a marginal linear-stability curve. It is found tha t the walking three-dimensional spatiotemporal solitons are dynamically sta ble in most cases; hence in principle they may be experimentally generated in quadratically nonlinear media.