Hamiltonian Methods in the Theory of Solitons
Hamiltonian Methods in the Theory of Solitons

Author: Ludwig Faddeev

Publisher: Springer Science & Business Media

Published: 2007-08-10

Total Pages: 602

ISBN-13: 3540699694

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The main characteristic of this classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schrödinger equation is considered as a main example, forming the first part of the book. The second part examines such fundamental models as the sine-Gordon equation and the Heisenberg equation, the classification of integrable models and methods for constructing their solutions.

Basic Methods Of Soliton Theory
Basic Methods Of Soliton Theory

Author: Ivan V Cherednik

Publisher: World Scientific

Published: 1996-08-22

Total Pages: 264

ISBN-13: 9814499005

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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 in Mathematics and Physics
Solitons in Mathematics and Physics

Author: Alan C. Newell

Publisher: SIAM

Published: 1985-06-01

Total Pages: 259

ISBN-13: 0898711967

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A discussion of the soliton, focusing on the properties that make it physically ubiquitous and the soliton equation mathematically miraculous.

Important Developments in Soliton Theory
Important Developments in Soliton Theory

Author: A.S. Fokas

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 563

ISBN-13: 3642580459

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In the last ten to fifteen years there have been many important developments in the theory of integrable equations. This period is marked in particular by the strong impact of soliton theory in many diverse areas of mathematics and physics; for example, algebraic geometry (the solution of the Schottky problem), group theory (the discovery of quantum groups), topology (the connection of Jones polynomials with integrable models), and quantum gravity (the connection of the KdV with matrix models). This is the first book to present a comprehensive overview of these developments. Numbered among the authors are many of the most prominent researchers in the field.

Integrable Hamiltonian Hierarchies
Integrable Hamiltonian Hierarchies

Author: Vladimir Gerdjikov

Publisher: Springer Science & Business Media

Published: 2008-06-02

Total Pages: 645

ISBN-13: 3540770534

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This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their hierarchies.

Soliton Equations and Hamiltonian Systems
Soliton Equations and Hamiltonian Systems

Author: L.A. Dickey

Publisher: World Scientific

Published: 1991

Total Pages: 328

ISBN-13: 9789810236847

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The theory of soliton equations and integrable systems has developed rapidly during the last 20 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 followed one single work by Gardner, Greene, Kruskal, and Miura about the Korteweg-de Vries equation (KdV) which, had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water.

Solitons
Solitons

Author: P. G. Drazin

Publisher: Cambridge University Press

Published: 1989-02-09

Total Pages: 244

ISBN-13: 9780521336550

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

Spectral Methods in Soliton Equations
Spectral Methods in Soliton Equations

Author: I D Iliev

Publisher: CRC Press

Published: 1994-11-21

Total Pages: 412

ISBN-13: 9780582239630

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Soliton theory as a method for solving some classes of nonlinear evolution equations (soliton equations) is one of the most actively developing topics in mathematical physics. This book presents some spectral theory methods for the investigation of soliton equations ad the inverse scattering problems related to these equations. The authors give the theory of expansions for the Sturm-Liouville operator and the Dirac operator. On this basis, the spectral theory of recursion operators generating Korteweg-de Vries type equations is presented and the Ablowitz-Kaup-Newell-Segur scheme, through which the inverse scattering method could be understood as a Fourier-type transformation, is considered. Following these ideas, the authors investigate some of the questions related to inverse spectral problems, i.e. uniqueness theorems, construction of explicit solutions and approximative methods for solving inverse scattering problems. A rigorous investigation of the stability of soliton solutions including solitary waves for equations which do not allow integration within inverse scattering method is also presented.

Soliton Theory
Soliton Theory

Author: Allan P. Fordy

Publisher: Manchester University Press

Published: 1990

Total Pages: 472

ISBN-13: 9780719014918

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A coherent introduction to the complete range of soliton theory including Hirota's method and Backlund transformations. Details physical applications of soliton theory with chapters on the peculiar wave patterns of the Andaman Sea, atmospheric phenomena, general relativity and Davydov solitons. Contains testing for full integrability, a discussion of the Painlevé technique, symmetries and conservation law.