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Lie Algebraic Methods In Integrable Systems
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Book Synopsis Lie Algebraic Methods in Integrable Systems by : Amit K. Roy-Chowdhury
Download or read book Lie Algebraic Methods in Integrable Systems written by Amit K. Roy-Chowdhury and published by CRC Press. This book was released on 2021-01-04 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last thirty years, the subject of nonlinear integrable systems has grown into a full-fledged research topic. In the last decade, Lie algebraic methods have grown in importance to various fields of theoretical research and worked to establish close relations between apparently unrelated systems. The various ideas associated with Lie algebra and Lie groups can be used to form a particularly elegant approach to the properties of nonlinear systems. In this volume, the author exposes the basic techniques of using Lie algebraic concepts to explore the domain of nonlinear integrable systems. His emphasis is not on developing a rigorous mathematical basis, but on using Lie algebraic methods as an effective tool. The book begins by establishing a practical basis in Lie algebra, including discussions of structure Lie, loop, and Virasor groups, quantum tori and Kac-Moody algebras, and gradation. It then offers a detailed discussion of prolongation structure and its representation theory, the orbit approach-for both finite and infinite dimension Lie algebra. The author also presents the modern approach to symmetries of integrable systems, including important new ideas in symmetry analysis, such as gauge transformations, and the "soldering" approach. He then moves to Hamiltonian structure, where he presents the Drinfeld-Sokolov approach, the Lie algebraic approach, Kupershmidt's approach, Hamiltonian reductions and the Gelfand Dikii formula. He concludes his treatment of Lie algebraic methods with a discussion of the classical r-matrix, its use, and its relations to double Lie algebra and the KP equation.
Book Synopsis Lie Algebraic Methods in Integrable Systems by : Amit K. Roy-Chowdhury
Download or read book Lie Algebraic Methods in Integrable Systems written by Amit K. Roy-Chowdhury and published by CRC Press. This book was released on 1999-09-28 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last thirty years, the subject of nonlinear integrable systems has grown into a full-fledged research topic. In the last decade, Lie algebraic methods have grown in importance to various fields of theoretical research and worked to establish close relations between apparently unrelated systems. The various ideas associated with Lie algebra and Lie groups can be used to form a particularly elegant approach to the properties of nonlinear systems. In this volume, the author exposes the basic techniques of using Lie algebraic concepts to explore the domain of nonlinear integrable systems. His emphasis is not on developing a rigorous mathematical basis, but on using Lie algebraic methods as an effective tool. The book begins by establishing a practical basis in Lie algebra, including discussions of structure Lie, loop, and Virasor groups, quantum tori and Kac-Moody algebras, and gradation. It then offers a detailed discussion of prolongation structure and its representation theory, the orbit approach-for both finite and infinite dimension Lie algebra. The author also presents the modern approach to symmetries of integrable systems, including important new ideas in symmetry analysis, such as gauge transformations, and the "soldering" approach. He then moves to Hamiltonian structure, where he presents the Drinfeld-Sokolov approach, the Lie algebraic approach, Kupershmidt's approach, Hamiltonian reductions and the Gelfand Dikii formula. He concludes his treatment of Lie algebraic methods with a discussion of the classical r-matrix, its use, and its relations to double Lie algebra and the KP equation.
Book Synopsis Lie Algebraic Methods in Integrable Systems by : A. Roy Chowdhury
Download or read book Lie Algebraic Methods in Integrable Systems written by A. Roy Chowdhury and published by Addison-Wesley Longman Limited. This book was released on 2000 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Integrable Systems of Classical Mechanics and Lie Algebras Volume I by : PERELOMOV
Download or read book Integrable Systems of Classical Mechanics and Lie Algebras Volume I written by PERELOMOV and published by Birkhäuser. This book was released on 2012-12-06 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a systematic presentation of a variety of methods and results concerning integrable systems of classical mechanics. The investigation of integrable systems was an important line of study in the last century, but up until recently only a small number of examples with two or more degrees of freedom were known. In the last fifteen years however, remarkable progress has been made in this field via the so-called isospectral deformation method which makes extensive use of group-theoretical concepts. The book focuses mainly on the development and applications of this new method, and also gives a fairly complete survey of the older classic results. Chapter 1 contains the necessary background material and outlines the isospectral deformation method in a Lie-algebraic form. Chapter 2 gives an account of numerous previously known integrable systems. Chapter 3 deals with many-body systems of generalized Calogero-Moser type, related to root systems of simple Lie algebras. Chapter 4 is devoted to the Toda lattice and its various modifications seen from the group-theoretic point of view. Chapter 5 investigates some additional topics related to many-body systems. The book will be valuable to students as well as researchers.
Book Synopsis Integrable Systems on Lie Algebras and Symmetric Spaces by : A. T. Fomenko
Download or read book Integrable Systems on Lie Algebras and Symmetric Spaces written by A. T. Fomenko and published by CRC Press. This book was released on 1988 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Second volume in the series, translated from the Russian, sets out new regular methods for realizing Hamilton's canonical equations in Lie algebras and symmetric spaces. Begins by constructing the algebraic embeddings in Lie algebras of Hamiltonian systems, going on to present effective methods for constructing complete sets of functions in involution on orbits of coadjoint representations of Lie groups. Ends with the proof of the full integrability of a wide range of many- parameter families of Hamiltonian systems that allow algebraicization. Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis Algebraic Integrability, Painlevé Geometry and Lie Algebras by : Mark Adler
Download or read book Algebraic Integrability, Painlevé Geometry and Lie Algebras written by Mark Adler and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Ergebnisse volume is aimed at a wide readership of mathematicians and physicists, graduate students and professionals. The main thrust of the book is to show how algebraic geometry, Lie theory and Painlevé analysis can be used to explicitly solve integrable differential equations and construct the algebraic tori on which they linearize; at the same time, it is, for the student, a playing ground to applying algebraic geometry and Lie theory. The book is meant to be reasonably self-contained and presents numerous examples. The latter appear throughout the text to illustrate the ideas, and make up the core of the last part of the book. The first part of the book contains the basic tools from Lie groups, algebraic and differential geometry to understand the main topic.
Book Synopsis Lectures on Integrable Systems by : Jens Hoppe
Download or read book Lectures on Integrable Systems written by Jens Hoppe and published by Springer Science & Business Media. This book was released on 2008-09-15 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mainly drawing on explicit examples, the author introduces the reader to themost recent techniques to study finite and infinite dynamical systems. Without any knowledge of differential geometry or lie groups theory the student can follow in a series of case studies the most recent developments. r-matrices for Calogero-Moser systems and Toda lattices are derived. Lax pairs for nontrivial infinite dimensionalsystems are constructed as limits of classical matrix algebras. The reader will find explanations of the approach to integrable field theories, to spectral transform methods and to solitons. New methods are proposed, thus helping students not only to understand established techniques but also to interest them in modern research on dynamical systems.
Book Synopsis Algebraic Methods and Lie Algebra Contractions by :
Download or read book Algebraic Methods and Lie Algebra Contractions written by and published by . This book was released on 1997 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Dynamical Systems VII by : V.I. Arnol'd
Download or read book Dynamical Systems VII written by V.I. Arnol'd and published by Springer Science & Business Media. This book was released on 2013-12-14 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of five surveys on dynamical systems, indispensable for graduate students and researchers in mathematics and theoretical physics. Written in the modern language of differential geometry, the book covers all the new differential geometric and Lie-algebraic methods currently used in the theory of integrable systems.
Book Synopsis Algebraic Methods in Physics by : Yvan Saint-Aubin
Download or read book Algebraic Methods in Physics written by Yvan Saint-Aubin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book pays tribute to two pioneers in the field of Mathematical physics, Jiri Patera and Pavel Winternitz of the CRM. Each has contributed more than forty years to the subject of mathematical physics, particularly to the study of algebraic methods.
Book Synopsis Integrable Systems of Classical Mechanics and Lie Algebras Volume I by : PERELOMOV
Download or read book Integrable Systems of Classical Mechanics and Lie Algebras Volume I written by PERELOMOV and published by Birkhäuser. This book was released on 1989-12-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed to expose from a general and universal standpoint a variety ofmethods and results concerning integrable systems ofclassical me- chanics. By such systems we mean Hamiltonian systems with a finite number of degrees of freedom possessing sufficiently many conserved quantities (in- tegrals ofmotion) so that in principle integration ofthe correspondingequa- tions of motion can be reduced to quadratures, i.e. to evaluating integrals of known functions. The investigation of these systems was an important line ofstudy in the last century which, among other things, stimulated the appearance of the theory ofLie groups. Early in our century, however, the work ofH. Poincare made it clear that global integrals of motion for Hamiltonian systems exist only in exceptional cases, and the interest in integrable systems declined. Until recently, only a small number ofsuch systems with two or more de- grees of freedom were known. In the last fifteen years, however, remarkable progress has been made in this direction due to the invention by Gardner, Greene, Kruskal, and Miura [GGKM 19671 ofa new approach to the integra- tion ofnonlinear evolution equations known as the inverse scattering method or the method of isospectral deformations. Applied to problems of mechanics this method revealed the complete in- tegrability of numerous classical systems. It should be pointed out that all systems of this kind discovered so far are related to Lie algebras, although often this relationship is not sosimpleas the oneexpressed by the well-known theorem of E. Noether.
Book Synopsis Integrable Systems of Classical Mechanics and Lie Algebras by : A. M. Perelomov
Download or read book Integrable Systems of Classical Mechanics and Lie Algebras written by A. M. Perelomov and published by Springer. This book was released on 1990 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a systematic presentation of a variety of methods and results concerning integrable systems of classical mechanics. The investigation of integrable systems was an important line of study in the last century, but up until recently only a small number of examples with two or more degrees of freedom were known. In the last fifteen years however, remarkable progress has been made in this field via the so-called isospectral deformation method which makes extensive use of group-theoretical concepts. The book focuses mainly on the development and applications of this new method, and also gives a fairly complete survey of the older classic results. Chapter 1 contains the necessary background material and outlines the isospectral deformation method in a Lie-algebraic form. Chapter 2 gives an account of numerous previously known integrable systems. Chapter 3 deals with many-body systems of generalized Calogero-Moser type, related to root systems of simple Lie algebras. Chapter 4 is devoted to the Toda lattice and its various modifications seen from the group-theoretic point of view. Chapter 5 investigates some additional topics related to many-body systems. The book will be valuable to students as well as researchers.
Book Synopsis Integrable Systems by : N. J. Hitchin
Download or read book Integrable Systems written by N. J. Hitchin and published by Oxford University Press. This book was released on 1999-03-18 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors. The authors are internationally renowned both as researchers and expositors, and the book is written in an informal and accessible style.
Book Synopsis Quantum Integrable Systems by : Asesh Roy Chowdhury
Download or read book Quantum Integrable Systems written by Asesh Roy Chowdhury and published by CRC Press. This book was released on 2004-01-28 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of integrable systems has opened new horizons in classical physics over the past few decades, particularly in the subatomic world. Yet despite the field now having reached a level of maturity, very few books provide an introduction to the field accessible to specialists and nonspecialists alike, and none offer a systematic survey of the m
Book Synopsis Dynamical Systems VII by : V.I. Arnol'd
Download or read book Dynamical Systems VII written by V.I. Arnol'd and published by Springer. This book was released on 2014-10-05 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of five surveys on dynamical systems, indispensable for graduate students and researchers in mathematics and theoretical physics. Written in the modern language of differential geometry, the book covers all the new differential geometric and Lie-algebraic methods currently used in the theory of integrable systems.
Book Synopsis Integrable systems of classical mechanics and Lie algebras by : Askolʹd M. Perelomov
Download or read book Integrable systems of classical mechanics and Lie algebras written by Askolʹd M. Perelomov and published by . This book was released on with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Classical Integrable Systems by : Olivier Babelon
Download or read book Introduction to Classical Integrable Systems written by Olivier Babelon and published by Cambridge University Press. This book was released on 2003-04-17 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough introduction to the theory of classical integrable systems, discussing the various approaches to the subject and explaining their interrelations. The book begins by introducing the central ideas of the theory of integrable systems, based on Lax representations, loop groups and Riemann surfaces. These ideas are then illustrated with detailed studies of model systems. The connection between isomonodromic deformation and integrability is discussed, and integrable field theories are covered in detail. The KP, KdV and Toda hierarchies are explained using the notion of Grassmannian, vertex operators and pseudo-differential operators. A chapter is devoted to the inverse scattering method and three complementary chapters cover the necessary mathematical tools from symplectic geometry, Riemann surfaces and Lie algebras. The book contains many worked examples and is suitable for use as a textbook on graduate courses. It also provides a comprehensive reference for researchers already working in the field.
