New exact solutions for cylindrical axisymmetric waves in a nonlinear nondispersive medium

We present a new method for deriving exact solutions of the Maxwell equations in a nonlinear medium without dispersion. It is assumed that the medium considered lacks a center of inversion and the dependence of the electric displacement on the electric field can be approximated by an exponential function. Using this method, a solution is obtained that describes the propagation of cylindrical electromagnetic waves in such a medium.