Some exact solutions of transient problems of electrodynamics in spherical coordinate system obtained by symmetry analysis of Klein-Gordon-Fock equation

Applying separation of variables to Maxwell equations in time domain one arrives to Klein-Gordon-Fock equation that describes radial wave propagation. The separation parameter for free space case has special form allowing the general solution to be found in exact form. For arbitrary separation parameter, which occurs in analysis of conical lines, the general solution is not suitable for calculations since it contains fractional derivatives. In this paper we obtain several families of exact solutions for this case using method of symmetry analysis of the equation.