General astigmatic nonparaxial wave beams and packets

We show that any solution of the paraxial parabolic equation can be simply transformed to some nonharmonic in time exact solution of the wave equation. On the basis of this observation, we generalize the known Bateman-type waves and present a family of exact solutions of the wave equation involving an arbitrary function, waveform. Argument of this function is much similar to that which appear in general astigmatic paraxial Gaussian beam. Special choices of the waveform allow general astigmatic beam-like and packetlike waves with Gaussian-type localization in space and time.