Integrable Hamiltonian Hierarchies

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Integrable Hamiltonian Hierarchies

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Author : Vladimir Gerdjikov
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-06-02

Integrable Hamiltonian Hierarchies written by Vladimir Gerdjikov 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 2008-06-02 with Science categories.

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.

Integrable Hamiltonian Hierarchies

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Author : Vladimir Gerdjikov
language : en
Publisher: Springer
Release Date : 2008-12-02

Integrable Hamiltonian Hierarchies written by Vladimir Gerdjikov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-02 with Science categories.

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.

Solitons In Mathematics And Physics

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Author : Alan C. Newell
language : en
Publisher: SIAM
Release Date : 1985-06-01

Solitons In Mathematics And Physics written by Alan C. Newell and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-06-01 with Technology & Engineering categories.

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

Integrable Hierarchies And Modern Physical Theories

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Author : Henrik Aratyn
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Integrable Hierarchies And Modern Physical Theories written by Henrik Aratyn 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 2012-12-06 with Science categories.

Proceedings of the NATO Advanced Research Workshop, Chicago, USA, July 22-26, 2000

Analytic Bilinear Approach To Integrable Hierarchies

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Author : L.V. Bogdanov
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-08-31

Analytic Bilinear Approach To Integrable Hierarchies written by L.V. Bogdanov 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 1999-08-31 with Science categories.

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.

Algebraic Structures In Integrability Foreword By Victor Kac

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Author : Vladimir V Sokolov
language : en
Publisher: World Scientific
Release Date : 2020-06-05

Algebraic Structures In Integrability Foreword By Victor Kac written by Vladimir V Sokolov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-05 with Science categories.

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.

Integrable Systems

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Author : Jean Louis Verdier
language : en
Publisher: Springer Science & Business Media
Release Date : 1993

Integrable Systems written by Jean Louis Verdier 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 1993 with Mathematics categories.

This book contains fifteen articles by eminent specialists in the theory of completely integrable systems, bringing together the diverse approaches to classical and quantum integrable systems and covering the principal current research developments.

Nonlinear Systems And Their Remarkable Mathematical Structures

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Author : Norbert Euler
language : en
Publisher: CRC Press
Release Date : 2021-09-07

Nonlinear Systems And Their Remarkable Mathematical Structures written by Norbert Euler and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-07 with Mathematics categories.

The third volume in this sequence of books consists of a collection of contributions that aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). Nonlinear Systems and Their Remarkable Mathematical Structures: Volume 3, Contributions from China just like the first two volumes, consists of contributions by world-leading experts in the subject of nonlinear systems, but in this instance only featuring contributions by leading Chinese scientists who also work in China (in some cases in collaboration with western scientists). Features Clearly illustrate the mathematical theories of nonlinear systems and its progress to both the non-expert and active researchers in this area Suitable for graduate students in Mathematics, Applied Mathematics and some of the Engineering sciences Written in a careful pedagogical manner by those experts who have been involved in the research themselves, and each contribution is reasonably self-contained

Quantum Theory And Symmetries

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Author : M. B. Paranjape
language : en
Publisher: Springer Nature
Release Date : 2021-03-26

Quantum Theory And Symmetries written by M. B. Paranjape and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-26 with Science categories.

This volume of the CRM Conference Series is based on a carefully refereed selection of contributions presented at the "11th International Symposium on Quantum Theory and Symmetries", held in Montréal, Canada from July 1-5, 2019. The main objective of the meeting was to share and make accessible new research and recent results in several branches of Theoretical and Mathematical Physics, including Algebraic Methods, Condensed Matter Physics, Cosmology and Gravitation, Integrability, Non-perturbative Quantum Field Theory, Particle Physics, Quantum Computing and Quantum Information Theory, and String/ADS-CFT. There was also a special session in honour of Decio Levi. The volume is divided into sections corresponding to the sessions held during the symposium, allowing the reader to appreciate both the homogeneity and the diversity of mathematical tools that have been applied in these subject areas. Several of the plenary speakers, who are internationally recognized experts in their fields, have contributed reviews of the main topics to complement the original contributions.

Computer Algebra And Geometric Algebra With Applications

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Author : Hongbo Li
language : en
Publisher: Springer
Release Date : 2005-06-20

Computer Algebra And Geometric Algebra With Applications written by Hongbo Li and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-20 with Computers categories.

MathematicsMechanization consistsoftheory,softwareandapplicationofc- puterized mathematical activities such as computing, reasoning and discovering. ItsuniquefeaturecanbesuccinctlydescribedasAAA(Algebraization,Algori- mization, Application). The name “Mathematics Mechanization” has its origin in the work of Hao Wang (1960s), one of the pioneers in using computers to do research in mathematics, particularly in automated theorem proving. Since the 1970s, this research direction has been actively pursued and extensively dev- oped by Prof. Wen-tsun Wu and his followers. It di?ers from the closely related disciplines like Computer Mathematics, Symbolic Computation and Automated Reasoning in that its goal is to make algorithmic studies and applications of mathematics the major trend of mathematics development in the information age. The International Workshop on Mathematics Mechanization (IWMM) was initiated by Prof. Wu in 1992, and has ever since been held by the Key L- oratory of Mathematics Mechanization (KLMM) of the Chinese Academy of Sciences. There have been seven workshops of the series up to now. At each workshop, several experts are invited to deliver plenary lectures on cutting-edge methods and algorithms of the selected theme. The workshop is also a forum for people working on related subjects to meet, collaborate and exchange ideas.