, X-waves are localized
solutions of the wave equation
that travel at a constant velocity
along a given direction.
X-waves can be sound, electromagnetic, or gravitational waves. They are built as a non-monochromatic superposition of Bessel beams.
X-waves carry infinite energy and travel superluminally (for electromagnetic waves). Finite energy realizations have been observed in various frameworks.
In optics, X-waves solutions have been also reported within a quantum mechanical formulation by A.Ciattoni and C.Conti in arxiv.org/abs/0704.0442v1