Waveguide Propagation of Nonlinear Waves

Waveguide Propagation of Nonlinear Waves PDF

Author: Sergey Leble

Publisher: Springer

Published: 2019-07-03

Total Pages: 288

ISBN-13: 3030226522

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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.

Schrödinger Equations in Nonlinear Systems

Schrödinger Equations in Nonlinear Systems PDF

Author: Wu-Ming Liu

Publisher: Springer

Published: 2019-03-20

Total Pages: 569

ISBN-13: 9811365814

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This book explores the diverse types of Schrödinger equations that appear in nonlinear systems in general, with a specific focus on nonlinear transmission networks and Bose–Einstein Condensates. In the context of nonlinear transmission networks, it employs various methods to rigorously model the phenomena of modulated matter-wave propagation in the network, leading to nonlinear Schrödinger (NLS) equations. Modeling these phenomena is largely based on the reductive perturbation method, and the derived NLS equations are then used to methodically investigate the dynamics of matter-wave solitons in the network. In the context of Bose–Einstein condensates (BECs), the book analyzes the dynamical properties of NLS equations with the external potential of different types, which govern the dynamics of modulated matter-waves in BECs with either two-body interactions or both two- and three-body interatomic interactions. It also discusses the method of investigating both the well-posedness and the ill-posedness of the boundary problem for linear and nonlinear Schrödinger equations and presents new results. Using simple examples, it then illustrates the results on the boundary problems. For both nonlinear transmission networks and Bose–Einstein condensates, the results obtained are supplemented by numerical calculations and presented as figures.

Nonlinear Wave Dynamics

Nonlinear Wave Dynamics PDF

Author: J. Engelbrecht

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 197

ISBN-13: 9401588910

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At the end of the twentieth century, nonlinear dynamics turned out to be one of the most challenging and stimulating ideas. Notions like bifurcations, attractors, chaos, fractals, etc. have proved to be useful in explaining the world around us, be it natural or artificial. However, much of our everyday understanding is still based on linearity, i. e. on the additivity and the proportionality. The larger the excitation, the larger the response-this seems to be carved in a stone tablet. The real world is not always reacting this way and the additivity is simply lost. The most convenient way to describe such a phenomenon is to use a mathematical term-nonlinearity. The importance of this notion, i. e. the importance of being nonlinear is nowadays more and more accepted not only by the scientific community but also globally. The recent success of nonlinear dynamics is heavily biased towards temporal characterization widely using nonlinear ordinary differential equations. Nonlinear spatio-temporal processes, i. e. nonlinear waves are seemingly much more complicated because they are described by nonlinear partial differential equations. The richness of the world may lead in this case to coherent structures like solitons, kinks, breathers, etc. which have been studied in detail. Their chaotic counterparts, however, are not so explicitly analysed yet. The wavebearing physical systems cover a wide range of phenomena involving physics, solid mechanics, hydrodynamics, biological structures, chemistry, etc.

Nonlinear Elastic Waves in Materials

Nonlinear Elastic Waves in Materials PDF

Author: Jeremiah J. Rushchitsky

Publisher: Springer Science & Business

Published: 2014-04-23

Total Pages: 445

ISBN-13: 3319004646

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The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professionally interesting in waves. But mechanics is understood in the broad sense, when it includes mechanical and other engineering, material science, applied mathematics and physics and so forth. The genesis of this book can be found in author’s years of research and teaching while a head of department at SP Timoshenko Institute of Mechanics (National Academy of Sciences of Ukraine), a member of Center for Micro and Nanomechanics at Engineering School of University of Aberdeen (Scotland) and a professor at Physical-Mathematical Faculty of National Technical University of Ukraine “KPI”. The book comprises 11 chapters. Each chapter is complemented by exercises, which can be used for the next development of the theory of nonlinear waves.

Theory of Waveguides and Transmission Lines

Theory of Waveguides and Transmission Lines PDF

Author: Edward F. Kuester

Publisher: CRC Press

Published: 2020-09-19

Total Pages: 611

ISBN-13: 1498730892

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This book covers the principles of operation of electromagnetic waveguides and transmission lines. The approach is divided between mathematical descriptions of basic behaviors and treatment of specific types of waveguide structures. Classical (distributed-network) transmission lines, their basic properties, their connection to lumped-element networks, and the distortion of pulses are discussed followed by a full field analysis of waveguide modes. Modes of specific kinds of waveguides - traditional hollow metallic waveguides, dielectric (including optical) waveguides, etc. are discussed. Problems of excitation and scattering of waveguide modes are addressed, followed by discussion of real systems and performance.

Waves Called Solitons

Waves Called Solitons PDF

Author: Michel Remoissenet

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 275

ISBN-13: 3662033216

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Encouraged by the friendly reception given to the first edition, I have preserved its basic form and most of the details. Apart from some corrections, minor changes, and addition of references where it was necessary, I have made the following changes. Chapter 1 was expanded by a discussion of the discovery of soli tons in the field of electromagnetic waves and optics. A new section devoted to nonlinear transmission lines and their applications in the microwave range has been added to Chap. 3. It seems to me that it was important to describe laboratory experiments on modulational instability, and subsequent generation of solitons, both in electrical transmission lines and in deep water in Chaps. 4 and 5. A description of a very simple experimental pocket version of the mechanical transmission line has been included in Chap. 6. Such a versatile and useful device should stimulate a practical approach to soli ton physics. Chapter 7 was completed by a short presentation of some recent experimental results on discrete Josephson transmission lines. A discussion of the experimental modulational instability of coupled optical waves and a simple look at quantum solitons were added to Chap. 8 in order to introduce the reader to such remarkable topics. Of the many people who made valuable comments on the first edition, I am particularly grateful to M. Dragoman, Y. S. Kivshar and A. W. Snyder. I would like to thank R. S. MacKay whose corrections and suggestions helped refine the manuscript of this second edition.

Ionization Waves in Electrical Breakdown of Gases

Ionization Waves in Electrical Breakdown of Gases PDF

Author: A.N. Lagarkov

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 237

ISBN-13: 1461242940

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In the years since the book of Lozanskii and Firsov "The Theory of Spark" [1975] was published, a number of experimental and theoretical studies in the physics of electric breakdown in gases were conducted. As a result of these studies, the concept of a wavelike nature of breakdown initiated by single high-voltage electric pulses or by a constant electric field was confirmed. Theoretical models in which the concept of breakdown in a constant external field was developed were first exposed in the above-named book in the chapter "Development of a streamer regarded as an ionization wave," written by Rodin and Starostin. This book treats the initial stage of electric breakdown as a wave pro cess. The wavelike nature of the phenomena under consideration is pre sented for streamers and sliding discharges, for electric breakdown develop ment in long discharge tubes as well as in gas-filled gaps. Chapter 1 gives a qualitative consideration of phenomena determin ing the electric breakdown of gases. The experimental data and theoretical results are exposed and discussed with application to streamers, plane ion ization waves, breakdown waves in long tubes, and propagation of sliding discharges. The subject of this chapter may be considered as an area of applications of different theoretical models, formulas, and estimates that are presented in other chapters of the book.

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