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Author: Vladimir Gerdjikov
Publisher: Springer Science & Business Media
ISBN: 3540770534
Category : Science
Languages : en
Pages : 645
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Book Description
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.
Author: Vladimir Gerdjikov
Publisher: Springer Science & Business Media
ISBN: 3540770534
Category : Science
Languages : en
Pages : 645
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Book Description
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.
Author: Henrik Aratyn
Publisher: Springer Science & Business Media
ISBN: 9401007209
Category : Science
Languages : en
Pages : 436
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Book Description
Proceedings of the NATO Advanced Research Workshop, Chicago, USA, July 22-26, 2000
Author: Yuri B. Suris
Publisher: Birkhäuser
ISBN: 3034880162
Category : Mathematics
Languages : en
Pages : 1078
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Book Description
An exploration of the theory of discrete integrable systems, with an emphasis on the following general problem: how to discretize one or several of independent variables in a given integrable system of differential equations, maintaining the integrability property? This question (related in spirit to such a modern branch of numerical analysis as geometric integration) is treated in the book as an immanent part of the theory of integrable systems, also commonly termed as the theory of solitons. Most of the results are only available from recent journal publications, many of them are new. Thus, the book is a kind of encyclopedia on discrete integrable systems. It unifies the features of a research monograph and a handbook. It is supplied with an extensive bibliography and detailed bibliographic remarks at the end of each chapter. Largely self-contained, it will be accessible to graduate and post-graduate students as well as to researchers in the area of integrable dynamical systems.
Author: Alan C. Newell
Publisher: SIAM
ISBN: 0898711967
Category : Technology & Engineering
Languages : en
Pages : 259
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Book Description
A discussion of the soliton, focusing on the properties that make it physically ubiquitous and the soliton equation mathematically miraculous.
Author: Boris A Kuperschmidt
Publisher: World Scientific
ISBN: 9814506737
Category : Science
Languages : en
Pages : 399
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Book Description
Some of the most active practitioners in the field of integrable systems have been asked to describe what they think of as the problems and results which seem to be most interesting and important now and are likely to influence future directions. The papers in this collection, representing their authors' responses, offer a broad panorama of the subject as it enters the 1990's.
Author: Vladimir Gerdjikov
Publisher: Springer
ISBN: 3540770542
Category : Science
Languages : en
Pages : 645
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Book Description
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.
Author: L.V. Bogdanov
Publisher: Springer Science & Business Media
ISBN: 9780792359197
Category : Science
Languages : en
Pages : 288
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Book Description
The subject of this book is the hierarchies of integrable equations connected with the one-component and multi component loop groups. There are many publications on this subject, and it is rather well defined. Thus, the author would like t.o explain why he has taken the risk of revisiting the subject. The Sato Grassmannian approach, and other approaches standard in this context, reveal deep mathematical structures in the base of the integrable hi erarchies. These approaches concentrate mostly on the algebraic picture, and they use a language suitable for applications to quantum field theory. Another well-known approach, the a-dressing method, developed by S. V. Manakov and V.E. Zakharov, is oriented mostly to particular systems and ex act classes of their solutions. There is more emphasis on analytic properties, and the technique is connected with standard complex analysis. The language of the a-dressing method is suitable for applications to integrable nonlinear PDEs, integrable nonlinear discrete equations, and, as recently discovered, for t.he applications of integrable systems to continuous and discret.e geometry. The primary motivation of the author was to formalize the approach to int.e grable hierarchies that was developed in the context of the a-dressing method, preserving the analytic struetures characteristic for this method, but omitting the peculiarit.ies of the construetive scheme. And it was desirable to find a start.
Author: L.A. Dickey
Publisher: World Scientific
ISBN: 9789810236847
Category : Science
Languages : en
Pages : 328
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Book Description
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.
Author: Yuri B. Suris
Publisher: Springer Science & Business Media
ISBN: 9783764369958
Category : Mathematics
Languages : en
Pages : 1118
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Book Description
An exploration of the theory of discrete integrable systems, with an emphasis on the following general problem: how to discretize one or several of independent variables in a given integrable system of differential equations, maintaining the integrability property? This question (related in spirit to such a modern branch of numerical analysis as geometric integration) is treated in the book as an immanent part of the theory of integrable systems, also commonly termed as the theory of solitons. Most of the results are only available from recent journal publications, many of them are new. Thus, the book is a kind of encyclopedia on discrete integrable systems. It unifies the features of a research monograph and a handbook. It is supplied with an extensive bibliography and detailed bibliographic remarks at the end of each chapter. Largely self-contained, it will be accessible to graduate and post-graduate students as well as to researchers in the area of integrable dynamical systems.
Author: Vladimir V Sokolov
Publisher: World Scientific
ISBN: 9811219664
Category : Science
Languages : en
Pages : 346
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Book Description
Relationships of the theory of integrable systems with various branches of mathematics are extremely deep and diverse. On the other hand, the most fundamental exactly integrable systems often have applications in theoretical physics. Therefore, many mathematicians and physicists are interested in integrable models.The book is intelligible to graduate and PhD students and can serve as an introduction to separate sections of the theory of classical integrable systems for scientists with algebraic inclinations. For the young, the book can serve as a starting point in the study of various aspects of integrability, while professional algebraists will be able to use some examples of algebraic structures, which appear in the theory of integrable systems, for wide-ranging generalizations.The statements are formulated in the simplest possible form. However, some ways of generalization are indicated. In the proofs, only essential points are mentioned, while for technical details, references are provided. The focus is on carefully selected examples. In addition, the book proposes many unsolved problems of various levels of complexity. A deeper understanding of every chapter of the book may require the study of more rigorous and specialized literature.
