Basic Methods Of Soliton Theory
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Basic Methods Of Soliton Theory
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Author : Ivan V Cherednik
language : en
Publisher: World Scientific
Release Date : 1996-08-22
Basic Methods Of Soliton Theory written by Ivan V Cherednik and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-08-22 with Science categories.
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.
Hamiltonian Methods In The Theory Of Solitons
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Author : Ludwig Faddeev
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-10
Hamiltonian Methods In The Theory Of Solitons written by Ludwig Faddeev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-10 with Science categories.
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.
Theory Of Solitons
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Author : S. Novikov
language : en
Publisher: Springer Science & Business Media
Release Date : 1984-05-31
Theory Of Solitons written by S. Novikov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-05-31 with Mathematics categories.
Soliton Theory And Its Applications
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Author : Chaohao Gu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Soliton Theory And Its Applications written by Chaohao Gu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
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.
The Direct Method In Soliton Theory
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Author : Ryogo Hirota
language : en
Publisher: Cambridge University Press
Release Date : 2004-07-22
The Direct Method In Soliton Theory written by Ryogo Hirota and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-07-22 with Mathematics categories.
Account of method of solving soliton equations by the inventor of the method.
Soliton Theory
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Author : Allan P. Fordy
language : en
Publisher: Manchester University Press
Release Date : 1990
Soliton Theory written by Allan P. Fordy and has been published by Manchester University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Evolution equations, Nonlinear categories.
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.
Solitons
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Author : R.K. Bullough
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Solitons written by R.K. Bullough and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Science categories.
With contributions by numerous experts
The Direct Method In Soliton Theory
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Author :
language : en
Publisher:
Release Date : 2004
The Direct Method In Soliton Theory written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Electronic books categories.
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.
Elements Of Soliton Theory
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Author : George L. Lamb
language : en
Publisher: John Wiley & Sons
Release Date : 1980
Elements Of Soliton Theory written by George L. Lamb and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Mathematics categories.
Spectral Methods In Soliton Equations
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Author : I D Iliev
language : en
Publisher: CRC Press
Release Date : 1994-11-21
Spectral Methods In Soliton Equations written by I D Iliev and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-11-21 with Mathematics categories.
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.