Waveguide Propagation of Nonlinear Waves : Impact of Inhomogeneity and Accompanying Effects

This book addresses the peculiarities of nonlinear wave propagation in waveguides and explains how the stratification depends on the waveguide and confinement. An example of this is an optical fibre that does not allow light to pass through a density jump. The book also discusses propagation in the nonlinear regime, which is characterized by a specific waveform and amplitude, to demonstrate so-called solitonic behaviour. In this case, a wave may be strongly localized, and propagates with a weak change in shape. In the waveguide case there are additional contributions of dispersion originating from boundary or asymptotic conditions.

Offering concrete guidance on solving application problems, this essentially (more than twice) expanded second edition includes various aspects of guided propagation of nonlinear waves as well as new topics like solitonic behaviour of one-mode and multi-mode excitation and propagation and plasma waveguides, propagation peculiarities of electromagnetic waves in metamaterials, new types of dispersion, dissipation, electromagnetic waveguides, planetary waves and plasma waves interaction.The key feature of the solitonic behaviour is based on Coupled KdV and Coupled NS systems. The systems are derived in this book and solved numerically with the proof of stability and convergence. The domain wall dynamics of ferromagnetic microwaveguides  and Bloch waves in nano-waveguides are also included with some problems of magnetic momentum and charge transport.

Sergey Leble earned his M.S. degree in Physics from the Department of Physics, State University of Saint Petersburg (former Leningrad) in 1968. He joined the Physics Department of Kaliningrad State University in the same year. He earned a Ph.D. degree in Theoretical and Mathematical Physics from the State University of Saint Petersburg in 1974. Working as an assistant professor, and later, as an associate professor he was awarded the Docent Diploma in 1979. He then assumed a postdoctoral research position and was awarded the Habilitation Diploma in 1987. He was appointed a professor in 1989.

In 1989 he was also elected as Head of the Theoretical Physics Department. He was subsequently invited as a visiting professor to Salamanca University, Spain (1994); the University of Gdansk, Poland (1995); Paderborn University, Germany (1997); Flemish University of Brussels, Belgium (1999), Utrecht University (2002); Loughborough University, Glasgow University, Imperial College of London,Birmingham University (2004), and the University of Antwerp (2016). After returning he was appointed a Professor at Emmanuel Kant Federal University (Russia, Kaliningrad).

Leble’s interests are centered on the nonlinear dynamics of solitary waves in different media and on their mathematical dimension – in nonlinear differential and difference equations, including their properties and explicit solutions. A focal point of this work concerns the applications of such tools and techniques as method for systems in physics (especially nonlinear optics and atomic physics) and environmental science. He has published over 200 research papers on nonlinear physics and applied mathematics, and authored and co-authored six books: “New Methods in Nonlinear Waves Theory”, “Nonlinear Waves in Waveguides with Stratification”, “Dressing Methods in Mathematical Physics”, “Nonlinear Waves in Optical Waveguides and Soliton Theory Application”, “Waveguide Electromagnetic Pulse Dynamics: Projecting Operators Method in: Odyssey of Light in Nonlinear Optical Fibers: Theory and Applications” and “Dynamical Projectors Method in Hydro- and Electrodynamics”.

Leble received numerous awards and distinctions for his work during his time at Kaliningrad and Gdansk. His research has been supported by numerous sources such as the Academy of Science (USSR), the RFFI (Russian Foundation for Fundamental Research), Ministry of Education, Kaliningrad and Gdansk Universities.

He currently teaches general and specialized courses in all areas of theoretical physics.