This book offers a rigorous and comprehensive study of nonlinear electromagnetic wave propagation in cylindrical dielectric waveguides with inhomogeneous and Kerr-type nonlinear media. It systematically develops mathematical models that describe the propagation of transverse electric (TE), transverse magnetic (TM), and hybrid waves in multilayered cylindrical structures, 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, hybrid wave behaviors, and multilayered media systems. 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 book is intended for applied mathematicians, physicists, and engineers working on 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. Readers will find the book to be an invaluable resource for extending their analytical and computational tools in nonlinear wave propagation.
