Applications of Lie Groups to Differential Equations : Graduate Texts in Mathematics - Peter J. Olver

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Applications of Lie Groups to Differential Equations

By: Peter J. Olver

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Paperback | 1 February 2000 | Edition Number 2

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Paperback
548 Pages

Edition Type
Revised

Dimensions(cm)
23.39 x 15.6 x 2.82

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Symmetry methods have long been recognized to be of great importance for the study of the differential equations. This book provides a solid introduction to those applications of Lie groups to differential equations which have proved to be useful in practice. The computational methods are presented so that graduate students and researchers can readily learn to use them. Following an exposition of the applications, the book develops the underlying theory. Many of the topics are presented in a novel way, with an emphasis on explicit examples and computations. Further examples, as well as new theoretical developments, appear in the exercises at the end of each chapter.

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Preface to First Edition
Preface to Second Edition
Acknowledgments
Introduction
Notes to the Reader
Introduction to Lie Groups	p. 1
Manifolds	p. 2
Lie Groups	p. 13
Vector Fields	p. 24
Lie Algebras	p. 42
Differential Forms	p. 53
Symmetry Groups of Differential Equations	p. 75
Symmetries of Algebraic Equations	p. 76
Groups and Differential Equations	p. 90
Prolongation	p. 94
Calculation of Symmetry Groups	p. 116
Integration of Ordinary Differential Equations	p. 130
Nondegeneracy Conditions for Differential Equations	p. 157
Group-Invariant Solutions	p. 183
Construction of Group-Invariant Solutions	p. 185
Examples of Group-Invariant Solutions	p. 190
Classification of Group-Invariant Solutions	p. 199
Quotient Manifolds	p. 209
Group-Invariant Prolongations and Reduction	p. 217
Symmetry Groups and Conservation Laws	p. 242
The Calculus of Variations	p. 243
Variational Symmetries	p. 252
Conservation Laws	p. 261
Noether's Theorem	p. 272
Generalized Symmetries	p. 286
Generalized Symmetries of Differential Equations	p. 288
Recursion Operators, Master Symmetries and Formal Symmetries	p. 304
Generalized Symmetries and Conservation Laws	p. 328
The Variational Complex	p. 350
Finite-Dimensional Hamiltonian Systems	p. 389
Poisson Brackets	p. 390
Symplectic Structures and Foliations	p. 398
Symmetries, First Integrals and Reduction of Order	p. 408
Hamiltonian Methods for Evolution Equations	p. 433
Poisson Brackets	p. 434
Symmetries and Conservation Laws	p. 446
Bi-Hamiltonian Systems	p. 452
References	p. 467
Symbol Index	p. 489
Author Index	p. 497
Subject Index	p. 501
Table of Contents provided by Blackwell. All Rights Reserved.

Applications of Lie Groups to Differential Equations

At a Glance

Paperback

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How to return your order

Defective items

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