Lie Equations
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Author |
: Peter J. Olver |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 524 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781468402742 |
ISBN-13 |
: 1468402749 |
Rating |
: 4/5 (42 Downloads) |
Synopsis Applications of Lie Groups to Differential Equations by : Peter J. Olver
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.
Author |
: Nailʹ Khaĭrullovich Ibragimov |
Publisher |
: John Wiley & Sons |
Total Pages |
: 376 |
Release |
: 1999-05-04 |
ISBN-10 |
: STANFORD:36105026109822 |
ISBN-13 |
: |
Rating |
: 4/5 (22 Downloads) |
Synopsis Elementary Lie Group Analysis and Ordinary Differential Equations by : Nailʹ Khaĭrullovich Ibragimov
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.
Author |
: Peter Ellsworth Hydon |
Publisher |
: Cambridge University Press |
Total Pages |
: 230 |
Release |
: 2000-01-28 |
ISBN-10 |
: 0521497868 |
ISBN-13 |
: 9780521497862 |
Rating |
: 4/5 (68 Downloads) |
Synopsis Symmetry Methods for Differential Equations by : Peter Ellsworth Hydon
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.
Author |
: Vladimir Dorodnitsyn |
Publisher |
: CRC Press |
Total Pages |
: 344 |
Release |
: 2010-12-01 |
ISBN-10 |
: 1420083104 |
ISBN-13 |
: 9781420083101 |
Rating |
: 4/5 (04 Downloads) |
Synopsis Applications of Lie Groups to Difference Equations by : Vladimir Dorodnitsyn
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
Author |
: Antonio Kumpera |
Publisher |
: Princeton University Press |
Total Pages |
: 316 |
Release |
: 1972-10-21 |
ISBN-10 |
: 0691081115 |
ISBN-13 |
: 9780691081113 |
Rating |
: 4/5 (15 Downloads) |
Synopsis Lie Equations by : Antonio Kumpera
In this monograph the authors redevelop the theory systematically using two different approaches. A general mechanism for the deformation of structures on manifolds was developed by Donald Spencer ten years ago. A new version of that theory, based on the differential calculus in the analytic spaces of Grothendieck, was recently given by B. Malgrange. The first approach adopts Malgrange's idea in defining jet sheaves and linear operators, although the brackets and the non-linear theory arc treated in an essentially different manner. The second approach is based on the theory of derivations, and its relationship to the first is clearly explained. The introduction describes examples of Lie equations and known integrability theorems, and gives applications of the theory to be developed in the following chapters and in the subsequent volume.
Author |
: Nail H. Ibragimov |
Publisher |
: CRC Press |
Total Pages |
: 572 |
Release |
: 1995-10-24 |
ISBN-10 |
: 0849394198 |
ISBN-13 |
: 9780849394195 |
Rating |
: 4/5 (98 Downloads) |
Synopsis CRC Handbook of Lie Group Analysis of Differential Equations by : Nail H. Ibragimov
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.
Author |
: L Dresner |
Publisher |
: CRC Press |
Total Pages |
: 242 |
Release |
: 1998-01-01 |
ISBN-10 |
: 1420050788 |
ISBN-13 |
: 9781420050783 |
Rating |
: 4/5 (88 Downloads) |
Synopsis Applications of Lie's Theory of Ordinary and Partial Differential Equations by : L Dresner
Lie's group theory of differential equations unifies the many ad hoc methods known for solving differential equations and provides powerful new ways to find solutions. The theory has applications to both ordinary and partial differential equations and is not restricted to linear equations. Applications of Lie's Theory of Ordinary and Partial Differential Equations provides a concise, simple introduction to the application of Lie's theory to the solution of differential equations. The author emphasizes clarity and immediacy of understanding rather than encyclopedic completeness, rigor, and generality. This enables readers to quickly grasp the essentials and start applying the methods to find solutions. The book includes worked examples and problems from a wide range of scientific and engineering fields.
Author |
: W.-H. Steeb |
Publisher |
: World Scientific |
Total Pages |
: 380 |
Release |
: 1996 |
ISBN-10 |
: 9810228910 |
ISBN-13 |
: 9789810228910 |
Rating |
: 4/5 (10 Downloads) |
Synopsis Continuous Symmetries, Lie Algebras, Differential Equations, and Computer Algebra by : W.-H. Steeb
This book is a comprehensive introduction to the application of continuous symmetries and their Lie algebras to ordinary and partial differential equations. It is suitable for students and research workers whose main interest lies in finding solutions to differential equations. It therefore caters for readers primarily interested in applied mathematics and physics rather than pure mathematics.The book provides an application-orientated text that is reasonably self-contained. A large number of worked examples have been included to help readers working independently of a teacher. The advance of algebraic computation has made it possible to write programs for the tedious calculations in this research field, and thus the book also makes a survey of computer algebra packages.
Author |
: Fritz Schwarz |
Publisher |
: CRC Press |
Total Pages |
: 446 |
Release |
: 2007-10-02 |
ISBN-10 |
: 9781584888901 |
ISBN-13 |
: 1584888903 |
Rating |
: 4/5 (01 Downloads) |
Synopsis Algorithmic Lie Theory for Solving Ordinary Differential Equations by : Fritz Schwarz
Despite the fact that Sophus Lie's theory was virtually the only systematic method for solving nonlinear ordinary differential equations (ODEs), it was rarely used for practical problems because of the massive amount of calculations involved. But with the advent of computer algebra programs, it became possible to apply Lie theory to concrete proble
Author |
: Robert Gilmore |
Publisher |
: Cambridge University Press |
Total Pages |
: 5 |
Release |
: 2008-01-17 |
ISBN-10 |
: 9781139469074 |
ISBN-13 |
: 113946907X |
Rating |
: 4/5 (74 Downloads) |
Synopsis Lie Groups, Physics, and Geometry by : Robert Gilmore
Describing many of the most important aspects of Lie group theory, this book presents the subject in a 'hands on' way. Rather than concentrating on theorems and proofs, the book shows the applications of the material to physical sciences and applied mathematics. Many examples of Lie groups and Lie algebras are given throughout the text. The relation between Lie group theory and algorithms for solving ordinary differential equations is presented and shown to be analogous to the relation between Galois groups and algorithms for solving polynomial equations. Other chapters are devoted to differential geometry, relativity, electrodynamics, and the hydrogen atom. Problems are given at the end of each chapter so readers can monitor their understanding of the materials. This is a fascinating introduction to Lie groups for graduate and undergraduate students in physics, mathematics and electrical engineering, as well as researchers in these fields.