  In recent experiments, localized and stationary pulses have been generated in
second-order nonlinear processes with femtosecond pulses, whose asymptotic
features relate with those of nondiffracting and nondispersing polychromatic
Bessel beams in linear dispersive media. We investigate on the nature of these
linear waves, and show that they can be identified with the X-shaped (O-shaped)
modes of the hyperbolic (elliptic) wave equation in media with normal
(anomalous) dispersion. Depending on the relative strengths of mode phase
mismatch, group velocity mismatch with respect to a plane pulse, and of the
defeated group velocity dispersion, these modes can adopt the form of pulsed
Bessel beams, focus wave modes, and X-waves (O-waves), respectively.
