Transforming of slowing laser beams to accelerating beams

We propose a method of obtaining solution of the paraxial Helmholtz equation which describes two-dimensional light beams accelerating on a finite interval of the trajectory. Method based on complex conjugation and shift along the longitudinal coordinate (parallel to the optical axis) of the complex amplitude of the slowing light beams. Using this method we obtained Fresnel and Laplace beams, as well as "half-Bessel" beams, accelerating along the trajectory in a form of square root. It has been observed that the well-known Hermite-Gaussian light beams are also accelerating beams with a hyperbolic trajectory. In contrast to well-known diffraction-free accelerating Airy beams all beams, which we consider, are converging upon propagation.