Continuous Symmetries, Lie Algebras, Differential Equations and Computer Algebra

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World Scientific Publishing Company, Sep 30, 1996 - Science - 372 pages
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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.

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Contents

Chapter 1 Introduction
1
Chapter 2 Groups
5
Chapter 3 Lie Groups and Lie Transformation Groups
17
Chapter 4 Infinitesimal Transformations
41
Chapter 5 Lie Algebras
57
Chapter 6 Introductory Examples
83
Chapter 7 Differential Forms and Tensor Fields
101
Chapter 8 Lie Derivative and Invariance
123
Chapter 13 Recursion Operators
219
Chapter 14 Backlund Transformations
233
Chapter 15 Lax Representations
241
Chapter 16 Conservation Laws
249
Chapter 17 Symmetries and Painleve Test
275
Chapter 18 Lie Algebra Valued Differential Forms
301
Chapter 19 Bose Operators and Lie Algebras
321
Chapter 20 Computer Algebra
331

Chapter 9 Invariance of Differential Equations
137
Chapter 10 LieBacklund Vector Fields
177
Chapter 11 Differential Equation for a Given Lie Algebra
191
Chapter 12 A List of Lie Symmetry Vector Fields
199
Appendix A Differentiable Manifolds
341
Bibliography
349
Index
357
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Common terms and phrases

admits analytic ຠApplications arbitrary associated assume basis bundle calculate called chapter commutator complex composition Computer Algebra condition Consequently conservation laws consider constant coordinates corresponding cosh defined Definition denoted depend determining differential forms dimension discussed element equivalent Example expansion exterior exterior derivative follows function give given GL(m identity independent infinitesimal Inserting integrable invariant inverse known Lie algebra Lie derivative Lie group Lie symmetry vector Lie-Bäcklund linear manifold matrix metric nonlinear Note obtain operator ordinary differential equations Painlevé test parameter partial differential equations prolongation REDUCE relations representation respect satisfies similarity sinh solution solve subgroup symmetry vector fields tensor field theorem transformation group valued variables vector space written

About the author (1996)

W-H Steeb (Rand Afrikaans University, South Africa)

Bibliographic information

QR code for Continuous Symmetries, Lie Algebras, Differential Equations and Computer Algebra
TitleContinuous Symmetries, Lie Algebras, Differential Equations and Computer Algebra
AuthorW-H Steeb
PublisherWorld Scientific Publishing Company, 1996
ISBN9813105038, 9789813105034
Length372 pages
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Science / Physics / Mathematical & Computational
  
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