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Time-Dependent One-Dimensional Electromagnetic Wave Propagation in Inhomogeneous Media: Exact Solution in Terms of Transmutations and Neumann Series of Bessel Functions
Lobachevskii Journal of Mathematics ( IF 0.8 ) Pub Date : 2020-07-27 , DOI: 10.1134/s1995080220050054 K. V. Khmelnytskaya , V. V. Kravchenko , S. M. Torba
中文翻译:
非均匀介质中随时间变化的一维电磁波传播:关于Trans变和贝塞尔函数的诺伊曼级数的精确解
更新日期:2020-07-27
Lobachevskii Journal of Mathematics ( IF 0.8 ) Pub Date : 2020-07-27 , DOI: 10.1134/s1995080220050054 K. V. Khmelnytskaya , V. V. Kravchenko , S. M. Torba
Abstract
The time-dependent Maxwell system describing electromagnetic wave propagation in inhomogeneous isotropic media in the one-dimensional case reduces to a Vekua-type equation for bicomplex-valued functions of a hyperbolic variable, see [7]. In [5] using this reduction a representation of a general solution of the system was obtained in terms of a couple of Darboux-associated transmutation operators [8]. In [6] a Fourier–Legendre expansion of transmutation integral kernels was obtained. This expansion is used in the present work for obtaining an exact solution of the problem of the transmission of a normally incident electromagnetic time-dependent plane wave through an arbitrary inhomogeneous layer. The result can be used for efficient computation of the transmitted modulated signals. In particular, it is shown that in the classical situation of a signal represented in terms of a trigonometric Fourier series the solution of the problem can be written in the form of Neumann series of Bessel functions with exact formulas for the coefficients. The representation lends itself to numerical computation.中文翻译:
非均匀介质中随时间变化的一维电磁波传播:关于Trans变和贝塞尔函数的诺伊曼级数的精确解