Description

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S.B. Leble's book deals with nonlinear waves and their propagation in metallic and dielectric waveguides and media with stratification. The underlying nonlinear evolution equations (NEEs) are derived giving also their solutions for specific situations. The reader will find new elements to the traditional approach. Various dispersion and relaxation laws for different guides are considered as well as the explicit form of projection operators, NEEs, quasi-solitons and of Darboux transforms. Special points relate to: 1. the development of a universal asymptotic method of deriving NEEs for guide propagation; 2. applications to the cases of stratified liquids, gases, solids and plasmas with various nonlinearities and dispersion laws; 3. connections between the basic problem and soliton- like solutions of the corresponding NEEs; 4. discussion of details of simple solutions in higher- order nonsingular perturbation theory.

About the Author

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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.