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

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.

preprint2013arXivOpen access
E. Yu. PetrovA. V. Kudrin
nlin.SIphysics.class-ph
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E. Yu. PetrovA. V. Kudrin

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