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The problem of longitudinal oscillations of an electric field and a charge polarization density in QED vacuum is considered. Within the framework of semiclassical analysis, we calculate time-periodic solutions of bosonized (1+1)-dimensional QED (massive Schwinger model). Applying the Bohr--Sommerfeld quantization condition, we determine the mass spectrum of charge-zero bound states (plasmons) which correspond in quantum theory to the found classical solutions. We show that the existence of such plasmons does not contradict any fundamental physical laws and study qualitatively their excitation in (3+1)-dimensional real world., Comment: 9 pages, 7 figures

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 analytical 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 take place only for linear oscillations and fields, can also be observed in the nonlinear oscillatory system., Comment: 7 pages, 2 figures

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., Comment: 5 pages, 3 figures

We present a new class of exact self-similar solutions possessing cylindrical or spherical symmetry in Born-Infeld theory. A cylindrically symmetric solution describes the propagation of a cylindrical electromagnetic disturbance in a constant background magnetic field in Born-Infeld electrodynamics. We show that this solution corresponds to vacuum breakdown and the subsequent propagation of an electron-positron avalanche. The proposed method of finding exact analytical solutions can be generalized to the model of a spherically symmetric scalar Born-Infeld field in the ($n+1$)-dimensional Minkowski space-time. As an example, the case $n=3$ is discussed., Comment: 5 pages, 4 figures

Many intriguing properties of driven nonlinear resonators, including the appearance of chaos, are very important for understanding the universal features of nonlinear dynamical systems and can have great practical significance. We consider a cylindrical cavity resonator driven by an alternating voltage and filled with a nonlinear nondispersive medium. It is assumed that the medium lacks a center of inversion and the dependence of the electric displacement on the electric field can be approximated by an exponential function. We show that the Maxwell equations are integrated exactly in this case and the field components in the cavity are represented in terms of implicit functions of special form. The driven electromagnetic oscillations in the cavity are found to display very interesting temporal behavior and their Fourier spectra contain singular continuous components. To the best of our knowledge, this is the first demonstration of the existence of a singular continuous (fractal) spectrum in an exactly integrable system., Comment: 5 pages, 3 figures