Basic Methods Of Soliton Theory

Author : Ivan V Cherednik
Publisher : World Scientific
Page : 264 pages
File Size : 40,6 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.

Author : Ludwig Faddeev,Leon Takhtajan
Publisher : Springer Science & Business Media
Page : 592 pages
File Size : 50,8 Mb
Release : 2007-08-10
Category : Science
ISBN : 9783540699699

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Hamiltonian Methods in the Theory of Solitons by Ludwig Faddeev,Leon Takhtajan Pdf

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.

Author : Chaohao Gu
Publisher : Springer Science & Business Media
Page : 414 pages
File Size : 43,6 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.

Author : S. Novikov,S.V. Manakov,L.P. Pitaevskii,V.E. Zakharov
Publisher : Springer Science & Business Media
Page : 298 pages
File Size : 51,9 Mb
Release : 1984-05-31
Category : Mathematics
ISBN : 0306109778

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Theory of Solitons by S. Novikov,S.V. Manakov,L.P. Pitaevskii,V.E. Zakharov Pdf

Author : Ryogo Hirota
Publisher : Cambridge University Press
Page : 220 pages
File Size : 51,8 Mb
Release : 2004-07-22
Category : Mathematics
ISBN : 0521836603

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The Direct Method in Soliton Theory by Ryogo Hirota Pdf

Account of method of solving soliton equations by the inventor of the method.

Author : R.K. Bullough,P.J. Caudrey
Publisher : Springer Science & Business Media
Page : 403 pages
File Size : 53,5 Mb
Release : 2013-11-11
Category : Science
ISBN : 9783642814488

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Solitons by R.K. Bullough,P.J. Caudrey Pdf

With contributions by numerous experts

Author : Allan P. Fordy
Publisher : Manchester University Press
Page : 472 pages
File Size : 50,9 Mb
Release : 1990
Category : Evolution equations, Nonlinear
ISBN : 0719014913

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Soliton Theory by Allan P. Fordy Pdf

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.

Author : Ligia Munteanu,Stefania Donescu
Publisher : Springer Science & Business Media
Page : 325 pages
File Size : 51,9 Mb
Release : 2006-07-06
Category : Mathematics
ISBN : 9781402025778

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Introduction to Soliton Theory: Applications to Mechanics by Ligia Munteanu,Stefania Donescu Pdf

This monograph is planned to provide the application of the soliton theory to solve certain practical problems selected from the fields of solid mechanics, fluid mechanics and biomechanics. The work is based mainly on the authors’ research carried out at their home institutes, and on some specified, significant results existing in the published literature. The methodology to study a given evolution equation is to seek the waves of permanent form, to test whether it possesses any symmetry properties, and whether it is stable and solitonic in nature. Students of physics, applied mathematics, and engineering are usually exposed to various branches of nonlinear mechanics, especially to the soliton theory. The soliton is regarded as an entity, a quasi-particle, which conserves its character and interacts with the surroundings and other solitons as a particle. It is related to a strange phenomenon, which consists in the propagation of certain waves without attenuation in dissipative media. This phenomenon has been known for about 200 years (it was described, for example, by the Joule Verne's novel Les histoires de Jean Marie Cabidoulin, Éd. Hetzel), but its detailed quantitative description became possible only in the last 30 years due to the exceptional development of computers. The discovery of the physical soliton is attributed to John Scott Russell. In 1834, Russell was observing a boat being drawn along a narrow channel by a pair of horses.

Author : A.S. Fokas,V.E. Zakharov
Publisher : Springer Science & Business Media
Page : 563 pages
File Size : 47,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642580451

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Important Developments in Soliton Theory by A.S. Fokas,V.E. Zakharov Pdf

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.

Author : Alex Kasman
Publisher : American Mathematical Soc.
Page : 322 pages
File Size : 54,6 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821852453

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Glimpses of Soliton Theory by Alex Kasman Pdf

Glimpses of Soliton Theory addresses some of the hidden mathematical connections in soliton theory which have been revealed over the last half-century. It aims to convince the reader that, like the mirrors and hidden pockets used by magicians, the underlying algebro-geometric structure of soliton equations provides an elegant and surprisingly simple explanation of something seemingly miraculous. --

Author : I D Iliev,Eugeni Khristov,Kiril Petrov Kirchev
Publisher : CRC Press
Page : 412 pages
File Size : 53,8 Mb
Release : 1994-11-21
Category : Mathematics
ISBN : 058223963X

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Spectral Methods in Soliton Equations by I D Iliev,Eugeni Khristov,Kiril Petrov Kirchev Pdf

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.

Author : David S. Ricketts,Donhee Ham
Publisher : CRC Press
Page : 191 pages
File Size : 41,5 Mb
Release : 2018-09-03
Category : Technology & Engineering
ISBN : 9781351833691

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Electrical Solitons by David S. Ricketts,Donhee Ham Pdf

The dominant medium for soliton propagation in electronics, nonlinear transmission line (NLTL) has found wide application as a testbed for nonlinear dynamics and KdV phenomena as well as for practical applications in ultra-sharp pulse/edge generation and novel nonlinear communication schemes in electronics. While many texts exist covering solitons in general, there is as yet no source that provides a comprehensive treatment of the soliton in the electrical domain. Drawing on the award winning research of Carnegie Mellon’s David S. Ricketts, Electrical Solitons Theory, Design, and Applications is the first text to focus specifically on KdV solitons in the nonlinear transmission line. Divided into three parts, the book begins with the foundational theory for KdV solitons, presents the core underlying mathematics of solitons, and describes the solution to the KdV equation and the basic properties of that solution, including collision behaviors and amplitude-dependent velocity. It also examines the conservation laws of the KdV for loss-less and lossy systems. The second part describes the KdV soliton in the context of the NLTL. It derives the lattice equation for solitons on the NLTL and shows the connection with the KdV equation as well as the governing equations for a lossy NLTL. Detailing the transformation between KdV theory and what we measure on the oscilloscope, the book demonstrates many of the key properties of solitons, including the inverse scattering method and soliton damping. The final part highlights practical applications such as sharp pulse formation and edge sharpening for high speed metrology as well as high frequency generation via NLTL harmonics. It describes challenges to realizing a robust soliton oscillator and the stability mechanisms necessary, and introduces three prototypes of the circular soliton oscillator using discrete and integrated platforms.

Author : Leonid A. Dickey
Publisher : World Scientific
Page : 428 pages
File Size : 45,7 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."

Author : G. Eilenberger
Publisher : Springer Science & Business Media
Page : 203 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642815096

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Solitons by G. Eilenberger Pdf

1.1 Why Study Solitons? The last century of physics, which was initiated by Maxwell's completion of the theory of electromagnetism, can, with some justification, be called the era of linear physi cs. ~Jith few excepti ons, the methods of theoreti ca 1 phys ics have been dominated by linear equations (Maxwell, Schrodinger), linear mathematical objects (vector spaces, in particular Hilbert spaces), and linear methods (Fourier transforms, perturbation theory, linear response theory) . Naturally the importance of nonlinearity, beginning with the Navier-Stokes equations and continuing to gravitation theory and the interactions of par ticles in solids, nuclei, and quantized fields, was recognized. However, it was hardly possible to treat the effects of nonlinearity, except as a per turbation to the basis solutions of the linearized theory. During the last decade, it has become more widely recognized in many areas of "field physics" that nonlinearity can result in qualitatively new phenom ena which cannot be constructed via perturbation theory starting from linear ized equations. By "field physics" we mean all those areas of theoretical physics for which the description of physical phenomena leads one to consider field equations, or partial differential equations of the form (1.1.1) ~t or ~tt = F(~, ~x ...) for one- or many-component "fields" Ht, x, y ...) (or their quantum analogs).

Author : Anonim
Publisher : Unknown
Page : 200 pages
File Size : 55,8 Mb
Release : 2004
Category : Electronic books
ISBN : 0511214847

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The Direct Method in Soliton Theory by Anonim Pdf

The modern version of the bilinear, or Hirota's direct, method is described here using relatively simple mathematics. As the only account in book form of the modern form of the theory, it will be essential reading for all those working in soliton theory.