  Plane waves in Kerr media spontaneously generate paraxial X-waves (i.e.
non-dispersive and non-diffractive pulsed beams) that get amplified along
propagation. This effect can be considered a form of conical emission (i.e.
spatio-temporal 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 spatio-temporal
localized wave patterns is identified. X-waves instability, and nonlinear
X-waves, are also expected in periodical Bose condensed gases.
