Nonlinear X-waves: light bullets in normally dispersive media?

Summary form only given. We show that a new type of nondiffracting and nondispersing nonlinear waves exist also for normal group velocity dispersion (GVD). Being the natural eigenmodes of the system, we believe that they are the key to understanding experiments where the diffraction, dispersion, and nonlinear length scales are comparable. Specifically, we consider the usual NLS model which describes the paraxial propagation of pulsed beams in Kerr media. In order to demonstrate the generality of X-waves as space-time localized solutions for normal GVD, we have extended our calculations to second-harmonic generation, where symbiotic two-color X-waves are found.