Airy-Tricomi-Gaussian compressed light bullets

Exact solution of the (3+1)D Schrödinger-type equation without external potential is obtained in cylindrical coordinates by using the method of separation of variables. Linear compressed light bullets are constructed with the help of a superposition of two counter-accelerating finite Airy wave functions and the Tricomi-Gaussian polynomials. We present some typical examples of the obtained solutions on the basis of four parameters: radial nodes, azimuthal nodes, the decay factor and the modulation depth. We find that the wave packets display different patterns and demonstrate that such linear light bullets can retain their shape over several Rayleigh lengths during propagation.