title: Exact solutions for the source-excited cylindrical electromagnetic waves in a nonlinear nondispersive medium.
abstract: The behavior of electromagnetic fields in nonlinear media has been a topical problem since the discovery of materials with a nonlinearity of electromagnetic properties. The problem of finding exact solutions for the source-excited nonlinear waves in curvilinear coordinates has been regarded as unsolvable for a long time. In this work, we present the first solution of this type for a cylindrically symmetric field excited by a pulsed current filament in a nondispersive medium that is simultaneously inhomogeneous and nonlinear. Assuming that the medium has a power-law permittivity profile in the linear regime and lacks a center of inversion, we derive an exact solution for the electromagnetic field excited by a current filament in such a medium and discuss the properties of this solution.
authors.affiliation: University of Nizhny Novgorod, 23 Gagarin Avenue, Nizhny Novgorod 603950, Russia.
authors.forename: V A
authors.initials: VA
authors.lastname: Es'kin
authors.forename: A V
authors.initials: AV
authors.lastname: Kudrin
authors.forename: E Yu
authors.initials: EY
authors.lastname: Petrov