Overview

This book offers a rigorous and comprehensive study of nonlinear electromagnetic wave propagation in the cylindrical Goubau line with inhomogeneous and Kerr-type nonlinear media. It systematically develops mathematical models that describe the propagation of transverse electric (TE), transverse magnetic (TM), and coupled TE–TM waves in the Goubau line configuration, where the dielectric permittivity depends on both the field intensity and the radial coordinate.   Key concepts explored here include nonlinear eigenvalue boundary-value problems, integral equations, and fixed-point techniques. The chapters cover topics such as nonlinear TE and TM modes, coupled TE–TM wave behaviors, and Goubau line configurations (including multilayer dielectric coatings). The author presents an expert analysis of these complex phenomena through a blend of analytical methods and numerical techniques, ensuring both mathematical rigor and physical insight. Theoretical results are supported by existence and uniqueness theorems, spectral analysis, and asymptotic estimates, while numerical approaches validate the analytical framework.   This monograph is intended for applied mathematicians, physicists, and engineers working in nonlinear electrodynamics, waveguide theory, and numerical modeling. It serves as both a research monograph and a reference text, with each chapter designed to be largely self-contained for flexible use by the reader. Researchers and students will find this book an invaluable resource for extending their analytical and computational tools in nonlinear wave propagation.

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9789819560004

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Eugen Smolkin is a lecturer in mathematics at the University of Gävle, Sweden. His current work mainly concentrates on wave-based inverse problems, adaptive finite element methods, and high-performance computing. He received his Ph.D. in applied mathematics in 2015 from the Marchuk Institute of Numerical Mathematics, Russian Academy of Science. His dissertation focused on nonlinear eigenvalue problems for TE and TM waves in cylindrical Kerr-type waveguides. From 2014 to 2022, he served as an associate professor at Penza State University, Russia, working on spectral methods for wave propagation in inhomogeneous and anisotropic media. He was also a guest researcher at the University of Gävle and Chalmers University of Technology, Sweden. Since 2019, he has been actively involved in international research projects such as WavES (Chalmers/GU) and the Network for Large-Scale Modeling. His research integrates theoretical analysis, numerical simulation, and scientific computing in electromagnetics.

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