General relativistic interaction of massless fields in cylindrical waves

In this paper the problem of finding exact solutions of the combined system of the Einstein-Maxwell-Weyl equations for cylindrical waves is reduced to the solution of two complete singular integral equations in the complex plane of the auxiliary analytical parameter. In the case of the nonsingular symmetry axis the problem further simplifies and requires solving the only integral equation, the expressions for the Ernst potentials on the symmetry axis then defining the group transformations of internal symmetries during the solution generation process. A large class of exact solutions for neutrino electrovacuum is obtained, and the Cauchy problem related to some particular initial data is considered