Generation and nonlinear dynamics of X waves of the Schrodinger equation

The generation of finite-energy packets of X waves is analyzed in normally dispersive cubic media by using an X-wave expansion. The three-dimensional nonlinear Schrödinger model is reduced to a one-dimensional equation with anomalous dispersion. Pulse splitting and beam replenishment as observed in experiments with water and Kerr media are explained in terms of a higher-order breathing soliton. The results presented also hold in periodic media and Bose-condensed gases.