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.
