Solitons, Nonlinear Evolution Equations and Inverse Scattering

Author: Mark J. Ablowitz,P. A. Clarkson

Publisher: Cambridge University Press

ISBN: 9780521387309

Category: Mathematics

Page: 516

View: 9115

This book brings together several aspects of soliton theory currently available only in research papers. Emphasis is given to the multi-dimensional problems which arise and includes inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multi-dimensions and the dbar method.

Solitons, Nonlinear Evolution Equations and Inverse Scattering

Author: M. A. Ablowitz,P. A. Clarkson

Publisher: Cambridge University Press

ISBN: 9780521387309

Category: Mathematics

Page: 532

View: 1736

This book brings together several aspects of soliton theory currently available only in research papers. Emphasis is given to the multi-dimensional problems which arise and includes inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multi-dimensions and the dbar method.

Direct and Inverse Methods in Nonlinear Evolution Equations

Lectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, September 5–12, 1999

Author: Robert M. Conte,Franco Magri,Micheline Musette,Junkichi Satsuma,Pavel Winternitz

Publisher: Springer Science & Business Media

ISBN: 9783540200871

Category: Science

Page: 279

View: 1172

Many physical phenomena are described by nonlinear evolution equation. Those that are integrable provide various mathematical methods, presented by experts in this tutorial book, to find special analytic solutions to both integrable and partially integrable equations. The direct method to build solutions includes the analysis of singularities à la Painlevé, Lie symmetries leaving the equation invariant, extension of the Hirota method, construction of the nonlinear superposition formula. The main inverse method described here relies on the bi-hamiltonian structure of integrable equations. The book also presents some extension to equations with discrete independent and dependent variables. The different chapters face from different points of view the theory of exact solutions and of the complete integrability of nonlinear evolution equations. Several examples and applications to concrete problems allow the reader to experience directly the power of the different machineries involved.

Solitons and the Inverse Scattering Transform

Author: Mark J. Ablowitz,Harvey Segur

Publisher: SIAM

ISBN: 089871477X

Category: Mathematics

Page: 425

View: 6277

A study, by two of the major contributors to the theory, of the inverse scattering transform and its application to problems of nonlinear dispersive waves that arise in fluid dynamics, plasma physics, nonlinear optics, particle physics, crystal lattice theory, nonlinear circuit theory and other areas. A soliton is a localised pulse-like nonlinear wave that possesses remarkable stability properties. Typically, problems that admit soliton solutions are in the form of evolution equations that describe how some variable or set of variables evolve in time from a given state. The equations may take a variety of forms, for example, PDEs, differential difference equations, partial difference equations, and integrodifferential equations, as well as coupled ODEs of finite order. What is surprising is that, although these problems are nonlinear, the general solution that evolves from almost arbitrary initial data may be obtained without approximation.

Nonlinear Evolution Equations and Soliton Solutions

Author: Yucui Guo

Publisher: N.A

ISBN: 9781634827690


Page: 530

View: 5155

This book studies the methods for solving non-linear, partial differential equations that have physical meaning, and soliton theory with applications. Specific descriptions on the formation mechanism of soliton solutions of non-linear, partial differential equations are given, and some methods for solving this kind of solution such as the Inverse Scattering Transform method, Backlund Transformation method, Similarity Reduction method and several kinds of function transformation methods are introduced. Integrability of non-linear, partial differential equations is also discussed. This book is suitable for graduate students whose research fields are in applied mathematics, applied physics and non-linear science-related directions as a textbook or a research reference book. This book is also useful for non-linear science researchers and teachers as a reference book. The characteristics of this book are: 1. The author provides clear concepts, rigorous derivation, thorough reasoning, and rigorous logic in the book. Since the research boom of non-linear, partial differential equations was rising in the 1960s, the research on non-linear, partial differential equations and soliton theory has only been several decades, which can be described as a very young discipline compared to the other branches in mathematics. Although there are a few related books, they are mostly in highly specialised interdisciplinary areas. There is no book which is suitable for cross-disciplines and for people with college level mathematics and college physics background. This book fills that gap; 2. The book is easy to be understood by readers since it provides step-by-step approaches. All results in the book have been deduced and collated by the author to make sure that they are correct and perfect; 3. The derivation from the physical models to mathematical models is emphasised in the book. In mathematical physics, we cannot just simply consider the mathematical problems without a physical image, which often plays the key role for understanding the mathematical problems; 4. Mathematical transformation methods are provided. The basic idea of various methods for solving non-linear, partial differential equations is to simplify the complex equations into simple ones through some transformations or decompositions. However, we cannot find any patterns for using such transformations or decompositions, and certain conjectures and assumptions have to be used. However, the skill and the logic of using the transformations and decompositions are very important to researchers in this field.

Nonlinear Evolution Equations And Dynamical Systems - Proceedings Of The 8th International Workshop (Needs '92)

Author: Makhankov Vladimir G,Pashaev O K,Puzynin I

Publisher: World Scientific

ISBN: 9814552895


Page: 504

View: 4802

This fascinating book presents the unusual career of a scientist of Chinese Malaysian origin, Ho Peng Yoke, who became a humanist and rendered his services to both Eastern and Western intellectual worlds. It describes how Ho adapted to working under changing social and academic environments in Singapore, Malaysia, Australia, Hong Kong and England. His activities also covered East Asia, Europe and North America.Ho Peng Yoke worked in collaboration with Joseph Needham of Cambridge over different periods spanning half a century in the monumental series Science and Civilization in China. Ho subsequently succeeded Needham as Director of the Needham Research Institute, where he held the post for 12 years. In the introduction to the final volume of that series, the Oxford scholar Mark Elvin remarked that Ho “had long piloted the ship through difficult times.” This book tells the story and more.

Nonlinear Evolution Equations and Dynamical Systems

Proceedings of the ICM 2002 Satellite Conference : Yellow Mountains, China 15-18 August 2002

Author: Yi Cheng

Publisher: World Scientific

ISBN: 9789812795366

Category: Differentiable dynamical systems

Page: 185

View: 1377

Fast-paced economic growth in Southeast Asia from the late 1960s until the mid-1990s brought increased attention to the overseas Chinese as an economically successful diaspora and their role in this economic growth. Events that followed, such as the transfer of Hong Kong and Macau to the People's Republic of China, the election of a non-KMT government in Taiwan, the Asian economic crisis and the plight of overseas Chinese in Indonesia as a result, and the durability of the Singapore economy during this same crisis, have helped to sustain this attention. The study of the overseas Chinese has by now become a global enterprise, raising new theoretical problems and empirical challenges. New case studies of overseas Chinese, such as those on communities in North America, Cuba, India, and South Africa, continually unveil different perspectives. New kinds of transnational connectivities linking Chinese communities are also being identified. It is now possible to make broader generalizations of a Chinese diaspora, on a global basis. Further, the intensifying study of the overseas Chinese has stimulated renewed intellectual vigor in other areas of research. The transnational and transregional activities of overseas Chinese, for example, pose serious challenges to analytical concepts of regional divides such as that between East and Southeast Asia. Despite the increased attention, new data, and the changing theoretical paradigms, basic questions concerning the overseas Chinese remain. The papers in this volume seek to understand the overseas Chinese migrants not just in terms of the overall Chinese diaspora per se, but also local Chinese migrants adapting to local societies, in different national contexts.

Odyssey of Light in Nonlinear Optical Fibers

Theory and Applications

Author: Kuppuswamy Porsezian,Ramanathan Ganapathy

Publisher: CRC Press

ISBN: 1351831100

Category: Science

Page: 568

View: 9301

Odyssey of Light in Nonlinear Optical Fibers: Theory and Applications presents a collection of breakthrough research portraying the odyssey of light from optical solitons to optical rogue waves in nonlinear optical fibers. The book provides a simple yet holistic view on the theoretical and application-oriented aspects of light, with a special focus on the underlying nonlinear phenomena. Exploring the very frontiers of light-wave technology, the text covers the basics of nonlinear fiberoptics and the dynamics of electromagnetic pulse propagation in nonlinear waveguides. It also highlights some of the latest advances in nonlinear optical fiber technology, discussing hidden symmetry reductions and Ablowitz–Kaup–Newell–Segur (AKNS) hierarchies for nonautonomous solitons, state-of-the-art Brillouin scattering applications, backpropagation, and the concept of eigenvalue communication—a powerful nonlinear digital signal processing technique that paves the way to overcome the current limitations of traditional communications methods in nonlinear fiber channels. Key chapters study the feasibility of the eigenvalue demodulation scheme based on digital coherent technology by throwing light on the experimental study of the noise tolerance of the demodulated eigenvalues, investigate matter wave solitons and other localized excitations pertaining to Bose–Einstein condensates in atom optics, and examine quantum field theory analogue effects occurring in binary waveguide arrays, plasmonic arrays, etc., as well as their ensuing nonlinear wave propagation. Featuring a foreword by Dr. Akira Hasegawa, the father of soliton communication systems, Odyssey of Light in Nonlinear Optical Fibers: Theory and Applications serves as a curtain raiser to usher in the photonics era. The technological innovations at the core of the book form the basis for the next generation of ultra-high speed computers and telecommunication devices.

Nonlinear Partial Differential Equations for Scientists and Engineers

Author: Lokenath Debnath

Publisher: Springer Science & Business Media

ISBN: 9780817682651

Category: Mathematics

Page: 860

View: 2200

The revised and enlarged third edition of this successful book presents a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied and updated applications. In an effort to make the book more useful for a diverse readership, updated modern examples of applications are chosen from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation. Nonlinear Partial Differential Equations for Scientists and Engineers, Third Edition, improves on an already highly complete and accessible resource for graduate students and professionals in mathematics, physics, science, and engineering. It may be used to great effect as a course textbook, research reference, or self-study guide.


Author: Boling Guo,Xiao-Feng Pang,Nan Liu,Yu-Feng Wang

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110549638

Category: Mathematics

Page: 376

View: 789

This book provides an up-to-date overview of mathematical theories and research results on solitons, presenting related mathematical methods and applications as well as numerical experiments. Different types of soliton equations are covered along with their dynamical behaviors and applications from physics, making the book an essential reference for researchers and graduate students in applied mathematics and physics. ContentsIntroductionInverse scattering transformAsymptotic behavior to initial value problems for some integrable evolution nonlinear equationsInteraction of solitons and its asymptotic propertiesHirota methodBäcklund transformations and the infinitely many conservation lawsMulti-dimensional solitons and their stabilityNumerical computation methods for some nonlinear evolution equationsThe geometric theory of solitonsGlobal existence and blow up for the nonlinear evolution equationsThe soliton movements of elementary particles in nonlinear quantum fieldThe theory of soliton movement of superconductive featuresThe soliton movements in condensed state systemsontents.

Discrete and Continuous Nonlinear Schrödinger Systems

Author: M. J. Ablowitz,B. Prinari,A. D. Trubatch

Publisher: Cambridge University Press

ISBN: 9780521534376

Category: Mathematics

Page: 257

View: 9000

This book presents a detailed mathematical analysis of scattering theory, obtains soliton solutions, and analyzes soliton interactions, both scalar and vector.

Introduction to Nonlinear Dispersive Equations

Author: Felipe Linares,Gustavo Ponce

Publisher: Springer

ISBN: 1493921819

Category: Mathematics

Page: 301

View: 3807

This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg–de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research. The second edition of Introduction to Nonlinear Dispersive Equations builds upon the success of the first edition by the addition of updated material on the main topics, an expanded bibliography, and new exercises. Assuming only basic knowledge of complex analysis and integration theory, this book will enable graduate students and researchers to enter this actively developing field.

Nonlinear Wave Equations

Author: Satyanad Kichenassamy

Publisher: CRC Press

ISBN: 9780824793289

Category: Science

Page: 296

View: 4876

This work examines the mathematical aspects of nonlinear wave propagation, emphasizing nonlinear hyperbolic problems. It introduces the tools that are most effective for exploring the problems of local and global existence, singularity formation, and large-time behaviour of solutions, and for the study of perturbation methods.


Author: R.K. Bullough,Philip Caudrey

Publisher: Springer Science & Business Media

ISBN: 3642814484

Category: Science

Page: 392

View: 3635

With contributions by numerous experts


Mathematical Methods for Physicists

Author: Guido Eilenberger

Publisher: Springer Science & Business Media

ISBN: 364281509X

Category: Science

Page: 194

View: 5425

Nonlinear Waves in Integrable and Nonintegrable Systems

Author: Jianke Yang

Publisher: SIAM

ISBN: 0898719682

Category: Nonlinear waves

Page: 430

View: 3842

Presents cutting-edge developments in the theory and experiments of nonlinear waves. Its comprehensive coverage of analytical and numerical methods for nonintegrable systems is the first of its kind.

Nonlinear Waves

Author: Lokenath Debnath

Publisher: CUP Archive

ISBN: 9780521254687

Category: Mathematics

Page: 360

View: 8511

The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.