Solitons In Mathematics And Physics

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Solitons in Mathematics and Physics

Alan C. Newell
Solitons in Mathematics and Physics Book PDF

Author : Alan C. Newell
Publisher : SIAM
Page : 260 pages
File Size : 53,7 Mb
Release : 1985-01-01
Category : Technology & Engineering
ISBN : 1611970229

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Solitons in Mathematics and Physics by Alan C. Newell Pdf

The soliton is a dramatic concept in nonlinear science. What makes this book unique in the treatment of this subject is its focus on the properties that make the soliton physically ubiquitous and the soliton equation mathematically miraculous. Here, on the classical level, is the entity field theorists have been postulating for years: a local traveling wave pulse; a lump-like coherent structure; the solution of a field equation with remarkable stability and particle-like properties. It is a fundamental mode of propagation in gravity- driven surface and internal waves; in atmospheric waves; in ion acoustic and Langmuir waves in plasmas; in some laser waves in nonlinear media; and in many biologic contexts, such as alpha-helix proteins.

Solitons

R. MacKenzie,M.B. Paranjape,W.J. Zakrzewski
Solitons Book PDF

Author : R. MacKenzie,M.B. Paranjape,W.J. Zakrzewski
Publisher : Springer Science & Business Media
Page : 308 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461212546

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Solitons by R. MacKenzie,M.B. Paranjape,W.J. Zakrzewski Pdf

Solitons were discovered by John Scott Russel in 1834, and have interested scientists and mathematicians ever since. They have been the subject of a large body of research in a wide variety of fields of physics and mathematics, not to mention engineering and other branches of science such as biology. This volume comprises the written versions of the talks presented at a workshop held at Queen's University in 1997, an interdisciplinary meeting wherein top researchers from many fields could meet, interact, and exchange ideas. Topics covered include mathematical and numerical aspects of solitons, as well as applications of solitons to nuclear and particle physics, cosmology, and condensed-matter physics. The book should be of interest to researchers in any field in which solitons are encountered.

Basic Methods Of Soliton Theory

Ivan V Cherednik
Basic Methods Of Soliton Theory Book PDF

Author : Ivan V Cherednik
Publisher : World Scientific
Page : 264 pages
File Size : 54,6 Mb
Release : 1996-08-22
Category : Science
ISBN : 9789814499002

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Basic Methods Of Soliton Theory by Ivan V Cherednik Pdf

In the 25 years of its existence Soliton Theory has drastically expanded our understanding of “integrability” and contributed a lot to the reunification of Mathematics and Physics in the range from deep algebraic geometry and modern representation theory to quantum field theory and optical transmission lines.The book is a systematic introduction to the Soliton Theory with an emphasis on its background and algebraic aspects. It is the first one devoted to the general matrix soliton equations, which are of great importance for the foundations and the applications.Differential algebra (local conservation laws, Bäcklund-Darboux transforms), algebraic geometry (theta and Baker functions), and the inverse scattering method (Riemann-Hilbert problem) with well-grounded preliminaries are applied to various equations including principal chiral fields, Heisenberg magnets, Sin-Gordon, and Nonlinear Schrödinger equation.

Solitons

Boling Guo,Xiao-Feng Pang,Yu-Feng Wang,Nan Liu
Solitons Book PDF

Author : Boling Guo,Xiao-Feng Pang,Yu-Feng Wang,Nan Liu
Publisher : Walter de Gruyter GmbH & Co KG
Page : 376 pages
File Size : 47,5 Mb
Release : 2018-03-19
Category : Mathematics
ISBN : 9783110549638

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Solitons by Boling Guo,Xiao-Feng Pang,Yu-Feng Wang,Nan Liu Pdf

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. Contents Introduction Inverse scattering transform Asymptotic behavior to initial value problems for some integrable evolution nonlinear equations Interaction of solitons and its asymptotic properties Hirota method Bäcklund transformations and the infinitely many conservation laws Multi-dimensional solitons and their stability Numerical computation methods for some nonlinear evolution equations The geometric theory of solitons Global existence and blow up for the nonlinear evolution equations The soliton movements of elementary particles in nonlinear quantum field The theory of soliton movement of superconductive features The soliton movements in condensed state systemsontents

The Versatile Soliton

Alexandre T. Filippov
The Versatile Soliton Book PDF

Author : Alexandre T. Filippov
Publisher : Springer Science & Business Media
Page : 261 pages
File Size : 54,7 Mb
Release : 2010-05-18
Category : Mathematics
ISBN : 9780817649746

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The Versatile Soliton by Alexandre T. Filippov Pdf

In this engaging book, the concept of the soliton is traced from the beginning of the last century to modern times with its recent applications.

Solitons in Physics, Mathematics, and Nonlinear Optics

Peter J. Olver,David H. Sattinger
Solitons in Physics Mathematics and Nonlinear Optics Book PDF

Author : Peter J. Olver,David H. Sattinger
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 43,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461390336

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Solitons in Physics, Mathematics, and Nonlinear Optics by Peter J. Olver,David H. Sattinger Pdf

This IMA Volume in Mathematics and its Applications SOLITONS IN PHYSICS, MATHEMATICS, AND NONLINEAR OPTICS is based on the proceedings of two workshops which were an integral part of the 1988-89 IMA program on NONLINEAR WAVES. The workshops focussed on the main parts of the theory of solitons and on the applications of solitons in physics, biology and engineering, with a special concentration on nonlinear optics. We thank the Coordinating Committee: James Glimm, Daniel Joseph, Barbara Keyfitz, An Majda, Alan Newell, Peter Olver, David Sattinger and David Schaeffer for drew planning and implementing the stimulating year-long program. We especially thank the Workshop Organizers for Solitons in Physics and Mathematics, Alan Newell, Peter Olver, and David Sattinger, and for Nonlinear Optics and Plasma Physics, David Kaup and Yuji Kodama for their efforts in bringing together many of the major figures in those research fields in which solitons in physics, mathematics, and nonlinear optics theories are used. A vner Friedman Willard Miller, Jr. PREFACE This volume includes some of the lectures given at two workshops, "Solitons in Physics and Mathematics" and "Solitons in Nonlinear Optics and Plasma Physics" held during the 1988-89 LM. A. year on Nonlinear Waves. Since their discovery by Kruskal and Zabusky in the early 1960's, solitons have had a profound impact on many fields, ranging from engineering and physics to algebraic geometry.

Solitons

Muthusamy Lakshmanan
Solitons Book PDF

Author : Muthusamy Lakshmanan
Publisher : Springer Science & Business Media
Page : 377 pages
File Size : 44,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642731938

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Solitons by Muthusamy Lakshmanan Pdf

A good deal of the material presented in this book has been prepared by top experts in the field lecturing in January 1987 at the Winter School on Solitons in Tiruchirapalli,India. The lectures begin at an elementary level but go on to include even the most recent developments in the field. The book makes a handy introduction to the various facets of the soliton concept, and will be useful both to newcomers to the field and to researchers who are interested in developments in new branches of physics and mathematics.

Solitons

P. G. Drazin
Solitons Book PDF

Author : P. G. Drazin
Publisher : Cambridge University Press
Page : 149 pages
File Size : 48,6 Mb
Release : 1983-07-21
Category : Mathematics
ISBN : 9780521274227

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Solitons by P. G. Drazin Pdf

A 'soliton' is a localized nonlinear wave of permanent form which may interact strongly with other solitons so that when they separate after the interaction they regain their original forms. This textbook is an account of the theory of solitons and of the diverse applications of the theory to nonlinear systems arising in the physical sciences. The essence of the book is an introduction to the method of inverse scattering. Solitary waves, cnoidal waves, conservation laws, the initial-value problem for the Korteweg-de Vries equation, the Lax method, the sine-Gordon equation and Backlund transformations are treated. The book will be useful for research workers who wish to learn about solitons as well as graduate students in mathematics, physics and engineering.

Soliton Theory and Its Applications

Chaohao Gu
Soliton Theory and Its Applications Book PDF

Author : Chaohao Gu
Publisher : Springer Science & Business Media
Page : 414 pages
File Size : 49,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662031025

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Soliton Theory and Its Applications by Chaohao Gu Pdf

Soliton theory is an important branch of applied mathematics and mathematical physics. An active and productive field of research, it has important applications in fluid mechanics, nonlinear optics, classical and quantum fields theories etc. This book presents a broad view of soliton theory. It gives an expository survey of the most basic ideas and methods, such as physical background, inverse scattering, Backlünd transformations, finite-dimensional completely integrable systems, symmetry, Kac-moody algebra, solitons and differential geometry, numerical analysis for nonlinear waves, and gravitational solitons. Besides the essential points of the theory, several applications are sketched and some recent developments, partly by the authors and their collaborators, are presented.

Soliton Phenomenology

V.G. Makhankov
Soliton Phenomenology Book PDF

Author : V.G. Makhankov
Publisher : Springer Science & Business Media
Page : 453 pages
File Size : 40,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400922174

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Soliton Phenomenology by V.G. Makhankov Pdf

'Et moi ..., si j'avait Sll comment en revemr, One service mathematics has rendered the je n'y serais point aIle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Soliton Equations and Hamiltonian Systems

Leonid A. Dickey
Soliton Equations and Hamiltonian Systems Book PDF

Author : Leonid A. Dickey
Publisher : World Scientific
Page : 428 pages
File Size : 44,9 Mb
Release : 2003
Category : Mathematics
ISBN : 9812794514

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Soliton Equations and Hamiltonian Systems by Leonid A. Dickey Pdf

The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics. For a long time, books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this output followed one single work by Gardner, Green, Kruskal, and Mizura on the Korteweg-de Vries equation (KdV), which had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water. Besides its obvious practical use, this theory is attractive also because it satisfies the aesthetic need in a beautiful formula which is so inherent to mathematics. The second edition is up-to-date and differs from the first one considerably. One third of the book (five chapters) is completely new and the rest is refreshed and edited. Contents: Integrable Systems Generated by Linear Differential n th Order Operators; Hamiltonian Structures; Hamiltonian Structure of the GD Hierarchies; Modified KdV and GD. The KupershmidtOCoWilson Theorem; The KP Hierarchy; Baker Function, a-Function; Additional Symmetries, String Equation; Grassmannian. Algebraic-Geometrical Krichever Solutions; Matrix First-Order Operator, AKNS-D Hierarchy; Generalization of the AKNS-D Hierarchy: Single-Pole and Multi-Pole Matrix Hierarchies; Isomonodromic Deformations and the Most General Matrix Hierarchy; Tau Functions of Matrix Hierarchies; KP, Modified KP, Constrained KP, Discrete KP, and q -KP; Another Chain of KP Hierarchies and Integrals Over Matrix Varieties; Transformational Properties of a Differential Operator under Diffeomorphisms and Classical W -Algebras; Further Restrictions of the KP, Stationary Equations; Stationary Equations of the Matrix Hierarchy; Field Lagrangian and Hamiltonian Formalism; Further Examples and Applications. Readership: Applied mathematicians and mathematical physicists."

Solitons

P. G. Drazin,R. S. Johnson
Solitons Book PDF

Author : P. G. Drazin,R. S. Johnson
Publisher : Cambridge University Press
Page : 240 pages
File Size : 43,8 Mb
Release : 1989-02-09
Category : Science
ISBN : 052133389X

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Solitons by P. G. Drazin,R. S. Johnson Pdf

Solitons: An Introduction discusses the theory of solitons and its diverse applications to nonlinear systems that arise in the physical sciences. Drazin and Johnson explain the generation and properties of solitons, introducing the mathematical technique known as the Inverse Scattering Tranform. Their aim is to present the essence of inverse scattering clearly, rather than rigorously or completely. Thus, the prerequisites are merely what is found in standard courses on mathematical physics and more advanced material is explained in the text with useful references to further reading given at the end of each chapter. Worked examples are frequently used to help the reader follow the various ideas and the exercises at the end of each chapter not only contain applications but also test understanding. Answers, or hints to their solution, are given at the end of the book. Sections and exercises that contain more difficult material are indicated by asterisks.

Solitons

P. G. Drazin,R. S. Johnson
Solitons Book PDF

Author : P. G. Drazin,R. S. Johnson
Publisher : Cambridge University Press
Page : 244 pages
File Size : 51,9 Mb
Release : 1989-02-09
Category : Mathematics
ISBN : 0521336554

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Solitons by P. G. Drazin,R. S. Johnson Pdf

This textbook is an introduction to the theory of solitons in the physical sciences.

Physics of Solitons

Thierry Dauxois,Michel Peyrard
Physics of Solitons Book PDF

Author : Thierry Dauxois,Michel Peyrard
Publisher : Cambridge University Press
Page : 435 pages
File Size : 50,5 Mb
Release : 2006-03-09
Category : Mathematics
ISBN : 9780521854214

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Physics of Solitons by Thierry Dauxois,Michel Peyrard Pdf

This textbook gives an instructive view of solitons and their applications for advanced students of physics.

Solitons, Instantons, and Twistors

Maciej Dunajski
Solitons Instantons and Twistors Book PDF

Author : Maciej Dunajski
Publisher : Oxford University Press
Page : 374 pages
File Size : 49,8 Mb
Release : 2010
Category : Mathematics
ISBN : 9780198570622

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Solitons, Instantons, and Twistors by Maciej Dunajski Pdf

A text aimed at third year undergraduates and graduates in mathematics and physics, presenting elementary twistor theory as a universal technique for solving differential equations in applied mathematics and theoretical physics.