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Author: M. Boiti
Publisher: World Scientific
Published: 2000
Total Pages: 576
ISBN-13: 9789810241476
DOWNLOAD EBOOKThis book discusses achievements in the last 20 years, recent developments and future perspectives in nonlinear science. Both continuous and discrete systems ? classical and quantum ? are considered.
Author: Mark J. Ablowitz
Publisher: World Scientific
Published: 2003
Total Pages: 438
ISBN-13: 9812382704
DOWNLOAD EBOOKThe theory of solitons involves a broad variety of mathematical methods and appears in many areas of physics, technology, biology, and pure and applied mathematics. In this book, emphasis is placed on both theory (considering mathematical approaches for classical and quantum nonlinear systems ? both continuous and discrete) and experiment (with special discussions on high bit rate optical communications and pulse dynamics in optical materials).
Author: Barbara Prinari
Publisher: World Scientific
Published: 2003-04-08
Total Pages: 438
ISBN-13: 9814486698
DOWNLOAD EBOOKThe theory of solitons involves a broad variety of mathematical methods and appears in many areas of physics, technology, biology, and pure and applied mathematics. In this book, emphasis is placed on both theory (considering mathematical approaches for classical and quantum nonlinear systems — both continuous and discrete) and experiment (with special discussions on high bit rate optical communications and pulse dynamics in optical materials).
Author: Decio Levi
Publisher: American Mathematical Society, Centre de Recherches Mathématiques
Published: 2023-01-23
Total Pages: 520
ISBN-13: 0821843540
DOWNLOAD EBOOKThis book on integrable systems and symmetries presents new results on applications of symmetries and integrability techniques to the case of equations defined on the lattice. This relatively new field has many applications, for example, in describing the evolution of crystals and molecular systems defined on lattices, and in finding numerical approximations for differential equations preserving their symmetries. The book contains three chapters and five appendices. The first chapter is an introduction to the general ideas about symmetries, lattices, differential difference and partial difference equations and Lie point symmetries defined on them. Chapter 2 deals with integrable and linearizable systems in two dimensions. The authors start from the prototype of integrable and linearizable partial differential equations, the Korteweg de Vries and the Burgers equations. Then they consider the best known integrable differential difference and partial difference equations. Chapter 3 considers generalized symmetries and conserved densities as integrability criteria. The appendices provide details which may help the readers' understanding of the subjects presented in Chapters 2 and 3. This book is written for PhD students and early researchers, both in theoretical physics and in applied mathematics, who are interested in the study of symmetries and integrability of difference equations.
Author: Kuppuswamy Porsezian
Publisher: Springer
Published: 2008-01-11
Total Pages: 411
ISBN-13: 3540361413
DOWNLOAD EBOOKOptical Solitons represent one of the most exciting and fascinating concepts in modern communications, arousing special interest due to their potential applications in optical fibre communication. This volume focuses on the explicit integration of analytical and experimental methods in nonlinear fibre optics and integrated optics. It covers all important recent technical issues in optical-soliton communication. For example, individual chapters are devoted to topics such as dispersion management and fibre Bragg grating. All authors are leading authorities in their fields.
Author: P. Tempesta, P. Winternitz, J. Harnad, W. Miller, Jr., G. Pogosyan, and M. Rodriguez
Publisher: American Mathematical Soc.
Published:
Total Pages: 364
ISBN-13: 9780821870327
DOWNLOAD EBOOKSuperintegrable systems are integrable systems (classical and quantum) that have more integrals of motion than degrees of freedom. Such systems have many interesting properties. This title is based on the Workshop on Superintegrability in Classical and Quantum Systems organized by the Centre de Recherches Mathematiques in Montreal (Quebec).
Author: Michael Grinfeld
Publisher: John Wiley & Sons
Published: 2015-01-12
Total Pages: 634
ISBN-13: 3527411887
DOWNLOAD EBOOKThe new edition is significantly updated and expanded. This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized. While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.
Author: Vladimir Dorodnitsyn
Publisher: CRC Press
Published: 2010-12-01
Total Pages: 344
ISBN-13: 9781420083101
DOWNLOAD EBOOKIntended for researchers, numerical analysts, and graduate students in various fields of applied mathematics, physics, mechanics, and engineering sciences, Applications of Lie Groups to Difference Equations is the first book to provide a systematic construction of invariant difference schemes for nonlinear differential equations. A guide to methods
Author: Sergey Leble
Publisher: Springer
Published: 2019-07-03
Total Pages: 298
ISBN-13: 3030226522
DOWNLOAD EBOOKThis 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.
