The features of propagation of intense waves are of great interest for theoryand experiment in electrodynamics and acoustics. The behavior of nonlinearwaves in a bounded volume is of especial importance and, at the same time, isan extremely complicated problem. It seems almost impossible to find a rigoroussolution to such a problem even for any model of nonlinearity. We obtain thefirst exact solution of this type. We present a new method for deriving exactsolutions of the Maxwell equations in a nonlinear medium without dispersion andgive examples of the obtained solutions that describe propagation ofcylindrical electromagnetic waves in a nonlinear nondispersive medium and freeelectromagnetic oscillations in a cylindrical cavity resonator filled with sucha medium.
展开▼