Es'kin V A, Kudrin A V, Petrov E Yu
University of Nizhny Novgorod, 23 Gagarin Avenue, Nizhny Novgorod 603950, Russia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jun;83(6 Pt 2):067602. doi: 10.1103/PhysRevE.83.067602. Epub 2011 Jun 29.
The behavior of electromagnetic fields in nonlinear media has been a topical problem since the discovery of materials with a nonlinearity of electromagnetic properties. The problem of finding exact solutions for the source-excited nonlinear waves in curvilinear coordinates has been regarded as unsolvable for a long time. In this work, we present the first solution of this type for a cylindrically symmetric field excited by a pulsed current filament in a nondispersive medium that is simultaneously inhomogeneous and nonlinear. Assuming that the medium has a power-law permittivity profile in the linear regime and lacks a center of inversion, we derive an exact solution for the electromagnetic field excited by a current filament in such a medium and discuss the properties of this solution.
自从发现具有电磁特性非线性的材料以来，非线性介质中电磁场的行为一直是一个热门问题。长期以来，在曲线坐标系中寻找源激发的非线性波的精确解的问题一直被认为是无法解决的。在这项工作中，我们给出了在非色散、同时非均匀且非线性的介质中，由脉冲电流细丝激发的圆柱对称场的此类首个解。假设该介质在线性区域具有幂律介电常数分布且缺乏反演中心，我们推导出了这种介质中电流细丝激发的电磁场的精确解，并讨论了该解的性质。
