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Applications Of Lie Groups To Difference Equations
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Book Synopsis Applications of Lie Groups to Differential Equations by : Peter J. Olver
Download or read book Applications of Lie Groups to Differential Equations written by Peter J. Olver and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to explaining a wide range of applications of con tinuous symmetry groups to physically important systems of differential equations. Emphasis is placed on significant applications of group-theoretic methods, organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems. The first chapter collects together (but does not prove) those aspects of Lie group theory which are of importance to differential equations. Applications covered in the body of the book include calculation of symmetry groups of differential equations, integration of ordinary differential equations, including special techniques for Euler-Lagrange equations or Hamiltonian systems, differential invariants and construction of equations with pre scribed symmetry groups, group-invariant solutions of partial differential equations, dimensional analysis, and the connections between conservation laws and symmetry groups. Generalizations of the basic symmetry group concept, and applications to conservation laws, integrability conditions, completely integrable systems and soliton equations, and bi-Hamiltonian systems are covered in detail. The exposition is reasonably self-contained, and supplemented by numerous examples of direct physical importance, chosen from classical mechanics, fluid mechanics, elasticity and other applied areas.
Book Synopsis Applications of Lie Groups to Difference Equations by : Vladimir Dorodnitsyn
Download or read book Applications of Lie Groups to Difference Equations written by Vladimir Dorodnitsyn and published by CRC Press. This book was released on 2010-12-01 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended for researchers, numerical analysts, and graduate students in various fields of applied mathematics, physics, mechanics, and engineering sciences, Applications of Lie Groups to Difference Equations is the first book to provide a systematic construction of invariant difference schemes for nonlinear differential equations. A guide to methods
Book Synopsis CRC Handbook of Lie Group Analysis of Differential Equations by : Nail H. Ibragimov
Download or read book CRC Handbook of Lie Group Analysis of Differential Equations written by Nail H. Ibragimov and published by CRC Press. This book was released on 1995-10-24 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: Today Lie group theoretical approach to differential equations has been extended to new situations and has become applicable to the majority of equations that frequently occur in applied sciences. Newly developed theoretical and computational methods are awaiting application. Students and applied scientists are expected to understand these methods. Volume 3 and the accompanying software allow readers to extend their knowledge of computational algebra. Written by the world's leading experts in the field, this up-to-date sourcebook covers topics such as Lie-Bäcklund, conditional and non-classical symmetries, approximate symmetry groups for equations with a small parameter, group analysis of differential equations with distributions, integro-differential equations, recursions, and symbolic software packages. The text provides an ideal introduction to modern group analysis and addresses issues to both beginners and experienced researchers in the application of Lie group methods.
Book Synopsis Symmetry Methods for Differential Equations by : Peter Ellsworth Hydon
Download or read book Symmetry Methods for Differential Equations written by Peter Ellsworth Hydon and published by Cambridge University Press. This book was released on 2000-01-28 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a straightforward introduction to the subject of symmetry methods for solving differential equations, and is aimed at applied mathematicians, physicists, and engineers. The presentation is informal, using many worked examples to illustrate the main symmetry methods. It is written at a level suitable for postgraduates and advanced undergraduates, and is designed to enable the reader to master the main techniques quickly and easily.The book contains some methods that have not previously appeared in a text. These include methods for obtaining discrete symmetries and integrating factors.
Book Synopsis Symmetries, Differential Equations and Applications by : Victor G. Kac
Download or read book Symmetries, Differential Equations and Applications written by Victor G. Kac and published by Springer. This book was released on 2018-11-04 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the third International Conference on Symmetries, Differential Equations and Applications (SDEA-III), this proceedings volume highlights recent important advances and trends in the applications of Lie groups, including a broad area of topics in interdisciplinary studies, ranging from mathematical physics to financial mathematics. The selected and peer-reviewed contributions gathered here cover Lie theory and symmetry methods in differential equations, Lie algebras and Lie pseudogroups, super-symmetry and super-integrability, representation theory of Lie algebras, classification problems, conservation laws, and geometrical methods. The SDEA III, held in honour of the Centenary of Noether’s Theorem, proven by the prominent German mathematician Emmy Noether, at Istanbul Technical University in August 2017 provided a productive forum for academic researchers, both junior and senior, and students to discuss and share the latest developments in the theory and applications of Lie symmetry groups. This work has an interdisciplinary appeal and will be a valuable read for researchers in mathematics, mechanics, physics, engineering, medicine and finance.
Book Synopsis Applications of Lie Groups to Differential Equations by : Peter J. Olver
Download or read book Applications of Lie Groups to Differential Equations written by Peter J. Olver and published by Springer Science & Business Media. This book was released on 1993 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: A solid introduction to applications of Lie groups to differential equations which have proved to be useful in practice. The computational methods are presented such that graduates and researchers can readily learn to use them. Following an exposition of the applications, the book develops the underlying theory, with many of the topics presented in a novel way, emphasising explicit examples and computations. Further examples, as well as new theoretical developments, appear in the exercises at the end of each chapter.
Book Synopsis Lie Groups, Lie Algebras, and Some of Their Applications by : Robert Gilmore
Download or read book Lie Groups, Lie Algebras, and Some of Their Applications written by Robert Gilmore and published by Courier Corporation. This book was released on 2012-05-23 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text introduces upper-level undergraduates to Lie group theory and physical applications. It further illustrates Lie group theory's role in several fields of physics. 1974 edition. Includes 75 figures and 17 tables, exercises and problems.
Book Synopsis Applications of Symmetry Methods to Partial Differential Equations by : George W. Bluman
Download or read book Applications of Symmetry Methods to Partial Differential Equations written by George W. Bluman and published by Springer Science & Business Media. This book was released on 2009-10-30 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an acessible book on the advanced symmetry methods for differential equations, including such subjects as conservation laws, Lie-Bäcklund symmetries, contact transformations, adjoint symmetries, Nöther's Theorem, mappings with some modification, potential symmetries, nonlocal symmetries, nonlocal mappings, and non-classical method. Of use to graduate students and researchers in mathematics and physics.
Book Synopsis Elementary Lie Group Analysis and Ordinary Differential Equations by : Nailʹ Khaĭrullovich Ibragimov
Download or read book Elementary Lie Group Analysis and Ordinary Differential Equations written by Nailʹ Khaĭrullovich Ibragimov and published by John Wiley & Sons. This book was released on 1999-05-04 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie group analysis, based on symmetry and invariance principles, is the only systematic method for solving nonlinear differential equations analytically. One of Lie's striking achievements was the discovery that the majority of classical devices for integration of special types of ordinary differential equations could be explained and deduced by his theory. Moreover, this theory provides a universal tool for tackling considerable numbers of differential equations when other means of integration fail. * This is the first modern text on ordinary differential equations where the basic integration methods are derived from Lie group theory * Includes a concise and self contained introduction to differential equations * Easy to follow and comprehensive introduction to Lie group analysis * The methods described in this book have many applications The author provides students and their teachers with a flexible text for undergraduate and postgraduate courses, spanning a variety of topics from the basic theory through to its many applications. The philosophy of Lie groups has become an essential part of the mathematical culture for anyone investigating mathematical models of physical, engineering and natural problems.
Book Synopsis An Introduction to Lie Groups and Lie Algebras by : Alexander A. Kirillov
Download or read book An Introduction to Lie Groups and Lie Algebras written by Alexander A. Kirillov and published by Cambridge University Press. This book was released on 2008-07-31 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.
Book Synopsis Nonlinear Symmetries and Nonlinear Equations by : G. Gaeta
Download or read book Nonlinear Symmetries and Nonlinear Equations written by G. Gaeta and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of (nonlinear) dift"erential equations was S. Lie's motivation when he created what is now known as Lie groups and Lie algebras; nevertheless, although Lie group and algebra theory flourished and was applied to a number of dift"erent physical situations -up to the point that a lot, if not most, of current fun damental elementary particles physics is actually (physical interpretation of) group theory -the application of symmetry methods to dift"erential equations remained a sleeping beauty for many, many years. The main reason for this lies probably in a fact that is quite clear to any beginner in the field. Namely, the formidable comple:rity ofthe (algebraic, not numerical!) computations involved in Lie method. I think this does not account completely for this oblivion: in other fields of Physics very hard analytical computations have been worked through; anyway, one easily understands that systems of dOlens of coupled PDEs do not seem very attractive, nor a very practical computational tool.
Book Synopsis Integrable Systems, Quantum Groups, and Quantum Field Theories by : Alberto Ibort
Download or read book Integrable Systems, Quantum Groups, and Quantum Field Theories written by Alberto Ibort and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many ways the last decade has witnessed a surge of interest in the interplay between theoretical physics and some traditional areas of pure mathematics. This book contains the lectures delivered at the NATO-ASI Summer School on `Recent Problems in Mathematical Physics' held at Salamanca, Spain (1992), offering a pedagogical and updated approach to some of the problems that have been at the heart of these events. Among them, we should mention the new mathematical structures related to integrability and quantum field theories, such as quantum groups, conformal field theories, integrable statistical models, and topological quantum field theories, that are discussed at length by some of the leading experts on the areas in several of the lectures contained in the book. Apart from these, traditional and new problems in quantum gravity are reviewed. Other contributions to the School included in the book range from symmetries in partial differential equations to geometrical phases in quantum physics. The book is addressed to researchers in the fields covered, PhD students and any scientist interested in obtaining an updated view of the subjects.
Book Synopsis Similarity Solutions of Nonlinear Partial Differential Equations by : Lawrence Dresner
Download or read book Similarity Solutions of Nonlinear Partial Differential Equations written by Lawrence Dresner and published by Pitman Advanced Publishing Program. This book was released on 1983 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Ordinary Differential Equations with Applications by : Carmen Chicone
Download or read book Ordinary Differential Equations with Applications written by Carmen Chicone and published by Springer Science & Business Media. This book was released on 2008-04-08 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a one-year course taught by the author to graduates at the University of Missouri, this book provides a student-friendly account of some of the standard topics encountered in an introductory course of ordinary differential equations. In a second semester, these ideas can be expanded by introducing more advanced concepts and applications. A central theme in the book is the use of Implicit Function Theorem, while the latter sections of the book introduce the basic ideas of perturbation theory as applications of this Theorem. The book also contains material differing from standard treatments, for example, the Fiber Contraction Principle is used to prove the smoothness of functions that are obtained as fixed points of contractions. The ideas introduced in this section can be extended to infinite dimensions.
Book Synopsis Symmetry and Integration Methods for Differential Equations by : George Bluman
Download or read book Symmetry and Integration Methods for Differential Equations written by George Bluman and published by Springer Science & Business Media. This book was released on 2008-01-10 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text discusses Lie groups of transformations and basic symmetry methods for solving ordinary and partial differential equations. It places emphasis on explicit computational algorithms to discover symmetries admitted by differential equations and to construct solutions resulting from symmetries. This new edition covers contact transformations, Lie-B cklund transformations, and adjoints and integrating factors for ODEs of arbitrary order.
Book Synopsis Lie Groups and Algebraic Groups by : Arkadij L. Onishchik
Download or read book Lie Groups and Algebraic Groups written by Arkadij L. Onishchik and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the notes of the authors' seminar on algebraic and Lie groups held at the Department of Mechanics and Mathematics of Moscow University in 1967/68. Our guiding idea was to present in the most economic way the theory of semisimple Lie groups on the basis of the theory of algebraic groups. Our main sources were A. Borel's paper [34], C. ChevalIey's seminar [14], seminar "Sophus Lie" [15] and monographs by C. Chevalley [4], N. Jacobson [9] and J-P. Serre [16, 17]. In preparing this book we have completely rearranged these notes and added two new chapters: "Lie groups" and "Real semisimple Lie groups". Several traditional topics of Lie algebra theory, however, are left entirely disregarded, e.g. universal enveloping algebras, characters of linear representations and (co)homology of Lie algebras. A distinctive feature of this book is that almost all the material is presented as a sequence of problems, as it had been in the first draft of the seminar's notes. We believe that solving these problems may help the reader to feel the seminar's atmosphere and master the theory. Nevertheless, all the non-trivial ideas, and sometimes solutions, are contained in hints given at the end of each section. The proofs of certain theorems, which we consider more difficult, are given directly in the main text. The book also contains exercises, the majority of which are an essential complement to the main contents.
Book Synopsis Basic Lie Theory by : Hossein Abbaspour
Download or read book Basic Lie Theory written by Hossein Abbaspour and published by World Scientific. This book was released on 2007 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a comprehensive treatment of basic Lie theory, primarily directed toward graduate study. The text is ideal for a full graduate course in Lie groups and Lie algebras. However, the book is also very usable for a variety of other courses: a one-semester course in Lie algebras, or on Haar measure and its applications, for advanced undergraduates; or as the text for one-semester graduate courses in Lie groups and symmetric spaces of non-compact type, or in lattices in Lie groups. The material is complete and detailed enough to be used for self-study; it can also serve as a reference work for professional mathematicians working in other areas. The book's utility for such a varied readership is enhanced by a diagram showing the interdependence of the separate chapters so that individual chapters and the material they depend upon can be selected, while others can be skipped.The book incorporates many of the most significant discoveries and pioneering contributions of the masters of the subject: Borel, Cartan, Chevalley, Iwasawa, Mostow, Siegel, and Weyl, among others.
