title: Exact axisymmetric solutions of the Maxwell equations in a nonlinear nondispersive medium.
abstract: The features of propagation of intense waves are of great interest for theory and experiment in electrodynamics and acoustics. The behavior of nonlinear waves in a bounded volume is of special importance and, at the same time, is an extremely complicated problem. It seems almost impossible to find a rigorous solution to such a problem even for any model of nonlinearity. We obtain the first exact solution of this type. We present a new method for deriving exact solutions of the Maxwell equations in a nonlinear medium without dispersion and give examples of the obtained solutions that describe propagation of cylindrical electromagnetic waves in a nonlinear nondispersive medium and free electromagnetic oscillations in a cylindrical cavity resonator filled with such a medium.
authors.affiliation: University of Nizhny Novgorod, 23 Gagarin Avenue, Nizhny Novgorod 603950, Russia.
authors.forename: E Yu
authors.initials: EY
authors.lastname: Petrov
authors.forename: A V
authors.initials: AV
authors.lastname: Kudrin