Algebraic Integrability Painleve Geometry And Lie Algebras PDF Download
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Author | : Mark Adler |
Publisher | : Springer Science & Business Media |
Total Pages | : 487 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 366205650X |
Download Algebraic Integrability, Painlevé Geometry and Lie Algebras Book in PDF, ePub and Kindle
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.
Author | : Mark Adler |
Publisher | : Springer |
Total Pages | : 502 |
Release | : 2014-01-15 |
Genre | : |
ISBN | : 9783662056516 |
Download Algebraic Integrability, Painleve Geometry and Lie Algebras Book in PDF, ePub and Kindle
Author | : Mark Adler |
Publisher | : Springer |
Total Pages | : 484 |
Release | : 2004-09-01 |
Genre | : Mathematics |
ISBN | : 9783540224709 |
Download Algebraic Integrability, Painlevé Geometry and Lie Algebras Book in PDF, ePub and Kindle
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.
Author | : Alexander Vitalievich Razumov |
Publisher | : Cambridge University Press |
Total Pages | : 271 |
Release | : 1997-05-15 |
Genre | : Mathematics |
ISBN | : 0521479231 |
Download Lie Algebras, Geometry, and Toda-Type Systems Book in PDF, ePub and Kindle
The book describes integrable Toda type systems and their Lie algebra and differential geometry background.
Author | : Ron Donagi |
Publisher | : Cambridge University Press |
Total Pages | : 421 |
Release | : 2020-04-02 |
Genre | : Mathematics |
ISBN | : 110880358X |
Download Integrable Systems and Algebraic Geometry: Volume 1 Book in PDF, ePub and Kindle
Created as a celebration of mathematical pioneer Emma Previato, this comprehensive book highlights the connections between algebraic geometry and integrable systems, differential equations, mathematical physics, and many other areas. The authors, many of whom have been at the forefront of research into these topics for the last decades, have all been influenced by Previato's research, as her collaborators, students, or colleagues. The diverse articles in the book demonstrate the wide scope of Previato's work and the inclusion of several survey and introductory articles makes the text accessible to graduate students and non-experts, as well as researchers. This first volume covers a wide range of areas related to integrable systems, often emphasizing the deep connections with algebraic geometry. Common themes include theta functions and Abelian varieties, Lax equations, integrable hierarchies, Hamiltonian flows and difference operators. These powerful tools are applied to spinning top, Hitchin, Painleve and many other notable special equations.
Author | : Lionel Mason |
Publisher | : Cambridge University Press |
Total Pages | : 170 |
Release | : 2003-11-20 |
Genre | : Mathematics |
ISBN | : 9780521529990 |
Download Geometry and Integrability Book in PDF, ePub and Kindle
Articles from leading researchers to introduce the reader to cutting-edge topics in integrable systems theory.
Author | : Amit K. Roy-Chowdhury |
Publisher | : CRC Press |
Total Pages | : 367 |
Release | : 2021-01-04 |
Genre | : Mathematics |
ISBN | : 1000116786 |
Download Lie Algebraic Methods in Integrable Systems Book in PDF, ePub and Kindle
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.
Author | : Pol Vanhaecke |
Publisher | : Springer Verlag |
Total Pages | : 240 |
Release | : 1996 |
Genre | : Mathematics |
ISBN | : |
Download Integrable Systems in the Realm of Algebraic Geometry Book in PDF, ePub and Kindle
2. Divisors and line bundles 97 2.1. Divisors . . 97 2.2. Line bundles 98 2.3. Sections of line bundles 99 2.4. The Riemann-Roch Theorem 101 2.5. Line bundles and embeddings in projective space 103 2.6. Hyperelliptic curves 104 3. Abelian varieties 106 3.1. Complex tori and Abelian varieties 106 3.2. Line bundles on Abelian varieties 107 3.3. Abelian surfaces 109 4. Jacobi varieties . . . 112 4.1. The algebraic Jacobian 112 4.2. The analytic/trancendental Jacobian 112 4.3. Abel's Theorem and Jacobi inversion 116 4.4. Jacobi and Kummer surfaces 118 4.5. Abelian surfaces of type (1.4) 120 V. Algebraic completely integrable Hamiltonian systems 123 1. Introduction . 123 2. A.c.i. systems 125 3. Painleve analysis for a.c.i. systems 131 4. Linearization of two-dimensional a.c.i. systems 134 5. Lax equations 136 VI. The master systems 139 1. Introduction . . . . .
Author | : Decio Levi |
Publisher | : Springer |
Total Pages | : 435 |
Release | : 2017-06-30 |
Genre | : Science |
ISBN | : 3319566660 |
Download Symmetries and Integrability of Difference Equations Book in PDF, ePub and Kindle
This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations. Difference equations are playing an increasingly important role in the natural sciences. Indeed, many phenomena are inherently discrete and thus naturally described by difference equations. More fundamentally, in subatomic physics, space-time may actually be discrete. Differential equations would then just be approximations of more basic discrete ones. Moreover, when using differential equations to analyze continuous processes, it is often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference ones. Each of the nine peer-reviewed chapters in this volume serves as a self-contained treatment of a topic, containing introductory material as well as the latest research results and exercises. Each chapter is presented by one or more early career researchers in the specific field of their expertise and, in turn, written for early career researchers. As a survey of the current state of the art, this book will serve as a valuable reference and is particularly well suited as an introduction to the field of symmetries and integrability of difference equations. Therefore, the book will be welcomed by advanced undergraduate and graduate students as well as by more advanced researchers.
Author | : Anthony W. Knapp |
Publisher | : Princeton University Press |
Total Pages | : 522 |
Release | : 1988-05-21 |
Genre | : Mathematics |
ISBN | : 069108498X |
Download Lie Groups, Lie Algebras, and Cohomology Book in PDF, ePub and Kindle
This book starts with the elementary theory of Lie groups of matrices and arrives at the definition, elementary properties, and first applications of cohomological induction, which is a recently discovered algebraic construction of group representations. Along the way it develops the computational techniques that are so important in handling Lie groups. The book is based on a one-semester course given at the State University of New York, Stony Brook in fall, 1986 to an audience having little or no background in Lie groups but interested in seeing connections among algebra, geometry, and Lie theory. These notes develop what is needed beyond a first graduate course in algebra in order to appreciate cohomological induction and to see its first consequences. Along the way one is able to study homological algebra with a significant application in mind; consequently one sees just what results in that subject are fundamental and what results are minor.