Integrability

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What Is Integrability?

Author : Vladimir E. Zakharov
Publisher : Springer Science & Business Media
ISBN 13 : 3642887031
Total Pages : 339 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis What Is Integrability? by : Vladimir E. Zakharov

Download or read book What Is Integrability? written by Vladimir E. Zakharov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea of devoting a complete book to this topic was born at one of the Workshops on Nonlinear and Turbulent Processes in Physics taking place reg ularly in Kiev. With the exception of E. D. Siggia and N. Ercolani, all authors of this volume were participants at the third of these workshops. All of them were acquainted with each other and with each other's work. Yet it seemed to be somewhat of a discovery that all of them were and are trying to understand the same problem - the problem of integrability of dynamical systems, primarily Hamiltonian ones with an infinite number of degrees of freedom. No doubt that they (or to be more exact, we) were led to this by the logical process of scientific evolution which often leads to independent, almost simultaneous discoveries. Integrable, or, more accurately, exactly solvable equations are essential to theoretical and mathematical physics. One could say that they constitute the "mathematical nucleus" of theoretical physics whose goal is to describe real clas sical or quantum systems. For example, the kinetic gas theory may be considered to be a theory of a system which is trivially integrable: the system of classical noninteracting particles. One of the main tasks of quantum electrodynamics is the development of a theory of an integrable perturbed quantum system, namely, noninteracting electromagnetic and electron-positron fields.

Integrability of Nonlinear Systems

Author : Yvette Kosmann-Schwarzbach
Publisher : Springer Science & Business Media
ISBN 13 : 9783540206309
Total Pages : 358 pages
Book Rating : 4.2/5 (63 download)

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Book Synopsis Integrability of Nonlinear Systems by : Yvette Kosmann-Schwarzbach

Download or read book Integrability of Nonlinear Systems written by Yvette Kosmann-Schwarzbach and published by Springer Science & Business Media. This book was released on 2004-02-17 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: The lectures that comprise this volume constitute a comprehensive survey of the many and various aspects of integrable dynamical systems. The present edition is a streamlined, revised and updated version of a 1997 set of notes that was published as Lecture Notes in Physics, Volume 495. This volume will be complemented by a companion book dedicated to discrete integrable systems. Both volumes address primarily graduate students and nonspecialist researchers but will also benefit lecturers looking for suitable material for advanced courses and researchers interested in specific topics.

Introduction to Classical Integrable Systems

Author : Olivier Babelon
Publisher : Cambridge University Press
ISBN 13 : 9780521822671
Total Pages : 622 pages
Book Rating : 4.8/5 (226 download)

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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.

Integrability

Author : Alexander Mikhailov
Publisher : Springer
ISBN 13 : 3540881115
Total Pages : 348 pages
Book Rating : 4.5/5 (48 download)

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Book Synopsis Integrability by : Alexander Mikhailov

Download or read book Integrability written by Alexander Mikhailov and published by Springer. This book was released on 2008-11-05 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principal aim of the book is to give a comprehensive account of the variety of approaches to such an important and complex concept as Integrability. Dev- oping mathematical models, physicists often raise the following questions: whether the model obtained is integrable or close in some sense to an integrable one and whether it can be studied in depth analytically. In this book we have tried to c- ate a mathematical framework to address these issues, and we give descriptions of methods and review results. In the Introduction we give a historical account of the birth and development of the theory of integrable equations, focusing on the main issue of the book – the concept of integrability itself. A universal de nition of Integrability is proving to be elusive despite more than 40 years of its development. Often such notions as “- act solvability” or “regular behaviour” of solutions are associated with integrable systems. Unfortunately these notions do not lead to any rigorous mathematical d- inition. A constructive approach could be based upon the study of hidden and rich algebraic or analytic structures associated with integrable equations. The requi- ment of existence of elements of these structures could, in principle, be taken as a de nition for integrability. It is astonishing that the nal result is not sensitive to the choice of the structure taken; eventually we arrive at the same pattern of eq- tions.

Elements of Classical and Quantum Integrable Systems

Author : Gleb Arutyunov
Publisher : Springer
ISBN 13 : 303024198X
Total Pages : 420 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Elements of Classical and Quantum Integrable Systems by : Gleb Arutyunov

Download or read book Elements of Classical and Quantum Integrable Systems written by Gleb Arutyunov and published by Springer. This book was released on 2019-07-23 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrable models have a fascinating history with many important discoveries that dates back to the famous Kepler problem of planetary motion. Nowadays it is well recognised that integrable systems play a ubiquitous role in many research areas ranging from quantum field theory, string theory, solvable models of statistical mechanics, black hole physics, quantum chaos and the AdS/CFT correspondence, to pure mathematics, such as representation theory, harmonic analysis, random matrix theory and complex geometry. Starting with the Liouville theorem and finite-dimensional integrable models, this book covers the basic concepts of integrability including elements of the modern geometric approach based on Poisson reduction, classical and quantum factorised scattering and various incarnations of the Bethe Ansatz. Applications of integrability methods are illustrated in vast detail on the concrete examples of the Calogero-Moser-Sutherland and Ruijsenaars-Schneider models, the Heisenberg spin chain and the one-dimensional Bose gas interacting via a delta-function potential. This book has intermediate and advanced topics with details to make them clearly comprehensible.

Integrability, Quantization, and Geometry: I. Integrable Systems

Author : Sergey Novikov
Publisher : American Mathematical Soc.
ISBN 13 : 1470455919
Total Pages : 516 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Integrability, Quantization, and Geometry: I. Integrable Systems by : Sergey Novikov

Download or read book Integrability, Quantization, and Geometry: I. Integrable Systems written by Sergey Novikov and published by American Mathematical Soc.. This book was released on 2021-04-12 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.

Integrability and Nonintegrability of Dynamical Systems

Author : Alain Goriely
Publisher : World Scientific
ISBN 13 : 981023533X
Total Pages : 435 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Integrability and Nonintegrability of Dynamical Systems by : Alain Goriely

Download or read book Integrability and Nonintegrability of Dynamical Systems written by Alain Goriely and published by World Scientific. This book was released on 2001 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book examines qualitative and quantitative methods for nonlinear differential equations, as well as integrability and nonintegrability theory. Starting from the idea of a constant of motion for simple systems of differential equations, it investigates the essence of integrability, its geometrical relevance and dynamical consequences. Integrability theory is approached from different perspectives, first in terms of differential algebra, then in terms of complex time singularities and finally from the viewpoint of phase geometry (for both Hamiltonian and non-Hamiltonian systems). As generic systems of differential equations cannot be exactly solved, the book reviews the different notions of nonintegrability and shows how to prove the nonexistence of exact solutions and/or a constant of motion. Finally, nonintegrability theory is linked to dynamical systems theory by showing how the property of complete integrability, partial integrability or nonintegrability can be related to regular and irregular dynamics in phase space.

Discrete Systems and Integrability

Author : J. Hietarinta
Publisher : Cambridge University Press
ISBN 13 : 1107042720
Total Pages : 461 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Discrete Systems and Integrability by : J. Hietarinta

Download or read book Discrete Systems and Integrability written by J. Hietarinta and published by Cambridge University Press. This book was released on 2016-09 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: A first introduction to the theory of discrete integrable systems at a level suitable for students and non-experts.

Global Aspects of Classical Integrable Systems

Author : Richard H. Cushman
Publisher : Birkhäuser
ISBN 13 : 3034809182
Total Pages : 493 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Global Aspects of Classical Integrable Systems by : Richard H. Cushman

Download or read book Global Aspects of Classical Integrable Systems written by Richard H. Cushman and published by Birkhäuser. This book was released on 2015-06-01 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a uniquely complete description of the geometry of the energy momentum mapping of five classical integrable systems: the 2-dimensional harmonic oscillator, the geodesic flow on the 3-sphere, the Euler top, the spherical pendulum and the Lagrange top. It presents for the first time in book form a general theory of symmetry reduction which allows one to reduce the symmetries in the spherical pendulum and the Lagrange top. Also the monodromy obstruction to the existence of global action angle coordinates is calculated for the spherical pendulum and the Lagrange top. The book addresses professional mathematicians and graduate students and can be used as a textbook on advanced classical mechanics or global analysis.

Integrability of Dynamical Systems: Algebra and Analysis

Author : Xiang Zhang
Publisher : Springer
ISBN 13 : 9811042268
Total Pages : 390 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Integrability of Dynamical Systems: Algebra and Analysis by : Xiang Zhang

Download or read book Integrability of Dynamical Systems: Algebra and Analysis written by Xiang Zhang and published by Springer. This book was released on 2017-03-30 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to systematically state the fundamental theory of integrability and its development of ordinary differential equations with emphasis on the Darboux theory of integrability and local integrability together with their applications. It summarizes the classical results of Darboux integrability and its modern development together with their related Darboux polynomials and their applications in the reduction of Liouville and elementary integrabilty and in the center—focus problem, the weakened Hilbert 16th problem on algebraic limit cycles and the global dynamical analysis of some realistic models in fields such as physics, mechanics and biology. Although it can be used as a textbook for graduate students in dynamical systems, it is intended as supplementary reading for graduate students from mathematics, physics, mechanics and engineering in courses related to the qualitative theory, bifurcation theory and the theory of integrability of dynamical systems.

An Introduction to Integrable Techniques for One-Dimensional Quantum Systems

Author : Fabio Franchini
Publisher : Springer
ISBN 13 : 3319484877
Total Pages : 186 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis An Introduction to Integrable Techniques for One-Dimensional Quantum Systems by : Fabio Franchini

Download or read book An Introduction to Integrable Techniques for One-Dimensional Quantum Systems written by Fabio Franchini and published by Springer. This book was released on 2017-05-25 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems. In a pedagogical way, a few examples of exactly solvable models are worked out to go from the coordinate approach to the Algebraic Bethe Ansatz, with some discussion on the finite temperature thermodynamics. The aim is to provide the instruments to approach more advanced books or to allow for a critical reading of research articles and the extraction of useful information from them. We describe the solution of the anisotropic XY spin chain; of the Lieb-Liniger model of bosons with contact interaction at zero and finite temperature; and of the XXZ spin chain, first in the coordinate and then in the algebraic approach. To establish the connection between the latter and the solution of two dimensional classical models, we also introduce and solve the 6-vertex model. Finally, the low energy physics of these integrable models is mapped into the corresponding conformal field theory. Through its style and the choice of topics, this book tries to touch all fundamental ideas behind integrability and is meant for students and researchers interested either in an introduction to later delve in the advance aspects of Bethe Ansatz or in an overview of the topic for broadening their culture.

Algebraic Integrability, Painlevé Geometry and Lie Algebras

Author : Mark Adler
Publisher : Springer Science & Business Media
ISBN 13 : 366205650X
Total Pages : 487 pages
Book Rating : 4.6/5 (62 download)

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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.

Symmetries and Integrability of Difference Equations

Author : Decio Levi
Publisher : Springer
ISBN 13 : 3319566660
Total Pages : 441 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Symmetries and Integrability of Difference Equations by : Decio Levi

Download or read book Symmetries and Integrability of Difference Equations written by Decio Levi and published by Springer. This book was released on 2017-06-30 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Aspects of Integrability of Differential Systems and Fields

Author : Costas J. Papachristou
Publisher : Springer Nature
ISBN 13 : 3030350029
Total Pages : 101 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Aspects of Integrability of Differential Systems and Fields by : Costas J. Papachristou

Download or read book Aspects of Integrability of Differential Systems and Fields written by Costas J. Papachristou and published by Springer Nature. This book was released on 2020-01-01 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as an introduction to the concept of integrability as it applies to systems of differential equations as well as to vector-valued fields. The author focuses on specific aspects of integrability that are often encountered in a variety of problems in applied mathematics, physics and engineering. The following general cases of integrability are examined: (a) path-independence of line integrals of vector fields on the plane and in space; (b) integration of a system of ordinary differential equations by using first integrals; and (c) integrable systems of partial differential equations. Special topics include the integration of analytic functions and some elements from the geometric theory of differential systems. Certain more advanced subjects, such as Lax pairs and Bäcklund transformations, are also discussed. The book is written at an intermediate level for educational purposes. The presentation is as simple as the topics allow, often sacrificing mathematical rigor in favor of pedagogical efficiency.

Integrability Theorems for Trigonometric Transforms

Author : Ralph P.Jr. Boas
Publisher : Springer Science & Business Media
ISBN 13 : 3642871089
Total Pages : 71 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Integrability Theorems for Trigonometric Transforms by : Ralph P.Jr. Boas

Download or read book Integrability Theorems for Trigonometric Transforms written by Ralph P.Jr. Boas and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is areport on the present state of a fairly coherent collection of problems about which a sizeable literature has grown up in recent years. In this literature, some of the problems have, as it happens, been analyzed in great detail, whereas other very similar ones have been treated much more superficially. I have not attempted to improve on the literature by making equally detailed presentations of every topic. I have also not aimed at encyclopedic completeness. I have, however, pointed out some possible generalizations by stating a number of questions; some of these could doubtless be disposed of in a few minutes; some are probably quite difficult. This monograph was written at the suggestion of B. SZ.-NAGY. I take this opportunity of pointing out that his paper [1] inspired the greater part of the material that is presented here; in particular, it contains the happy idea of focusing Y attention on the multipliers nY-i, x- . R. ASKEY, P. HEYWOOD, M. and S. IZUMI, and S. WAINGER have kindly communicated some of their recent results to me before publication. I am indebted for help on various points to L. S. BOSANQUET, S. M. EDMONDS, G. GOES, S. IZUMI, A. ZYGMUND, and especially to R. ASKEY. My work was supported by the National Science Foundation under grants GP-314, GP-2491, GP-3940 and GP-5558. Evanston, Illinois, February, 1967 R. P. Boas, Jr. Contents Notations ... § 1. Introduetion 3 §2. Lemmas .. 7 § 3. Theorems with positive or decreasing functions .

Architecting the Industrial Internet

Author : Shyam Nath
Publisher : Packt Publishing Ltd
ISBN 13 : 1787283747
Total Pages : 351 pages
Book Rating : 4.7/5 (872 download)

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Book Synopsis Architecting the Industrial Internet by : Shyam Nath

Download or read book Architecting the Industrial Internet written by Shyam Nath and published by Packt Publishing Ltd. This book was released on 2017-09-22 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learn the ins and outs of the Industrial Internet of Things through subjects ranging from its history and evolution, right up to what the future holds. About This Book Define solutions that can connect existing systems and newer cloud-based solutions to thousands of thousands of edge devices and industrial machines Identify, define, and justify Industrial Internet of Things (IIoT) projects, and design an application that can connect to and control thousands of machines Leverage the power and features of a platform to monitor, perform analytics, and maintain the Industrial Internet Who This Book Is For Architects who are interested in learning how to define solutions for the Industrial Internet will benefit immensely from this book. Relevant architect roles include enterprise architects, business architects, information architects, cloud solution architects, software architects, and others. The content is also relevant for technically inclined line of business leaders investing in these solutions. What You Will Learn Learn the history of the Industrial Internet and why an architectural approach is needed Define solutions that can connect to and control thousands of edge devices and machines Understand the significance of working with line of business leadership and key metrics to be gathered Connect business requirements to the functional architecture Gain the right expectation as to the capabilities of Industrial Internet applications and how to assess them Understand what data and analytics components should be included in your architecture solution Understand deployment trade-offs, management and security considerations, and the impact of emerging technologies In Detail The Industrial Internet or the IIoT has gained a lot of traction. Many leading companies are driving this revolution by connecting smart edge devices to cloud-based analysis platforms and solving their business challenges in new ways. To ensure a smooth integration of such machines and devices, sound architecture strategies based on accepted principles, best practices, and lessons learned must be applied. This book begins by providing a bird's eye view of what the IIoT is and how the industrial revolution has evolved into embracing this technology. It then describes architectural approaches for success, gathering business requirements, and mapping requirements into functional solutions. In a later chapter, many other potential use cases are introduced including those in manufacturing and specific examples in predictive maintenance, asset tracking and handling, and environmental impact and abatement. The book concludes by exploring evolving technologies that will impact IIoT architecture in the future and discusses possible societal implications of the Industrial Internet and perceptions regarding these projects. By the end of this book, you will be better equipped to embrace the benefits of the burgeoning IIoT. Style and approach This book takes a comprehensive approach to the Industrial Internet, thoroughly acquainting the reader with the concepts and philosophy of the IIoT. It provides a basis for defining an IIoT solution in a thoughtful manner and creating what will be viewed as a successful project.

Probability: A Graduate Course

Author : Allan Gut
Publisher : Springer Science & Business Media
ISBN 13 : 0387273328
Total Pages : 617 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Probability: A Graduate Course by : Allan Gut

Download or read book Probability: A Graduate Course written by Allan Gut and published by Springer Science & Business Media. This book was released on 2006-03-16 with total page 617 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook on the theory of probability starts from the premise that rather than being a purely mathematical discipline, probability theory is an intimate companion of statistics. The book starts with the basic tools, and goes on to cover a number of subjects in detail, including chapters on inequalities, characteristic functions and convergence. This is followed by explanations of the three main subjects in probability: the law of large numbers, the central limit theorem, and the law of the iterated logarithm. After a discussion of generalizations and extensions, the book concludes with an extensive chapter on martingales.