title: Droplet-shaped waves: causal finite-support analogs of X-shaped waves.
abstract: A model of steady-state X-shaped wave generation by a superluminal (supersonic) pointlike source infinitely moving along a straight line is extended to a more realistic causal scenario of a source pulse launched at time zero and propagating rectilinearly at a constant superluminal speed. In the case of an infinitely short (delta) pulse, the new model yields an analytical solution, corresponding to the propagation-invariant X-shaped wave clipped by a droplet-shaped support, which perpetually expands along the propagation and transversal directions, thus tending the droplet-shaped wave to the X-shaped one.
authors.affiliation: INOVInesc Inovação and ICEMS, Instituto Superior Técnico, Technical University of Lisbon, Lisbon, Portugal. andrei.utkin@inov.pt
authors.forename: Andrei B
authors.initials: AB
authors.lastname: Utkin