Exact Axisymmetric Solutions of the Maxwell Equations in a Nonlinear Nondispersive Medium

TL;DR

This paper presents the first exact solutions to Maxwell's equations for cylindrical electromagnetic waves in a nonlinear, nondispersive medium, advancing understanding of wave behavior in complex nonlinear systems.

Contribution

It introduces a novel method for deriving exact solutions of Maxwell equations in nonlinear media, which was previously considered nearly impossible.

Findings

Exact solutions for cylindrical wave propagation

Solutions describing electromagnetic oscillations in a cavity

New method applicable to nonlinear nondispersive media

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 especial 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.