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ZhETF, Vol. 149, No. 6, p. 1149 (June 2016)
(English translation - JETP, Vol. 122, No. 6, p. 995, June 2016 available online at )

Nonlinear normal modes in electrodynamic systems: a nonperturbative approach
Kudrin A.V., Kudrina O.A., Petrov E.Yu.

Received: December 27, 2015

DOI: 10.7868/S0044451016060055

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We consider electromagnetic nonlinear normal modes in cylindrical cavity resonators filled with a nonlinear nondispersive medium. The key feature of the analysis is that exact analytic solutions of the nonlinear field equations are employed to study the mode properties in detail. Based on such a nonperturbative approach, we rigorously prove that the total energy of free nonlinear oscillations in a distributive conservative system, such as that considered in our work, can exactly coincide with the sum of energies of the normal modes of the system. This fact implies that the energy orthogonality property, which has so far been known to hold only for linear oscillations and fields, can also be observed in a nonlinear oscillatory system.

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