University of Nizhny Novgorod, 23 Gagarin Avenue, Nizhny Novgorod 603950, Russia.
Phys Rev Lett. 2010 May 14;104(19):190404. doi: 10.1103/PhysRevLett.104.190404.
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 special 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.
强波传播的特征在电动力学和声学的理论和实验中都具有重要意义。在有界体积中非线性波的行为特别重要，同时也是一个极其复杂的问题。即使对于任何非线性模型，找到这样一个问题的严格解似乎几乎是不可能的。我们得到了第一个这样的精确解。我们提出了一种新的方法，用于在没有色散的非线性介质中推导出麦克斯韦方程组的精确解，并给出了描述圆柱形电磁在非线性非弥散介质中传播和填充这种介质的圆柱形腔谐振器中自由电磁振荡的所得到的解的例子。
