X-wave-mediated instability of plane waves in Kerr media

Plane waves in Kerr media spontaneously generate paraxial X-waves (i.e., nondispersive and nondiffractive pulsed beams) that get amplified along propagation. This effect can be considered to be a form of conical emission (i.e., spatiotemporal modulational instability), and can be used as a key for the interpretation of the out-of-axis energy emission in the splitting process of focused pulses in normally dispersive materials. A new class of spatiotemporal localized wave patterns is identified. X-wave instability and nonlinear X waves are predicted for both focusing and defocusing media and are expected in periodical Bose condensed gases.