Many intriguing properties of driven nonlinear resonators, including theappearance of chaos, are very important for understanding the universalfeatures of nonlinear dynamical systems and can have great practicalsignificance. We consider a cylindrical cavity resonator driven by analternating voltage and filled with a nonlinear nondispersive medium. It isassumed that the medium lacks a center of inversion and the dependence of theelectric displacement on the electric field can be approximated by anexponential function. We show that the Maxwell equations are integrated exactlyin this case and the field components in the cavity are represented in terms ofimplicit functions of special form. The driven electromagnetic oscillations inthe cavity are found to display very interesting temporal behavior and theirFourier spectra contain singular continuous components. To the best of ourknowledge, this is the first demonstration of the existence of a singularcontinuous (fractal) spectrum in an exactly integrable system.
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