Continuous Symmetries, Lie Algebras, Differential Equations And Computer AlgebraThis 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. |
Contents
| 1 | |
| 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 |
| 349 | |
| 357 | |
Other editions - View all
Continuous Symmetries, Lie Algebras, Differential Equations, and Computer ... W.-H. Steeb Limited preview - 1996 |
Common terms and phrases
Bäcklund transformation conservation laws conserved current consider coordinates cosh defined Definition denoted determining equations differential forms diffusion equation dx₁ element Example follows Gateaux derivative given GL(m infinitesimal integrable invariant inverse jet bundle Korteweg-de Vries equation Lie algebra Lie algebra valued Lie derivative Lie group Lie point symmetry Lie symmetry vector Lie-Bäcklund vector fields linear manifold matrix metric tensor metric tensor field nonlinear obtain one-form ordinary differential equations Painlevé test parameter partial differential equations point symmetry vector recursion operator sine-Gordon equation sinh smooth function solution subgroup symmetry vector fields tensor field theorem transformation group u₁ variables vector space x₁ θαι θα θε θυ θψ λ λ λεΚ ΣΣ ди ди ди ди дх2 диг диз диј дх дхг дхз მ მ მ