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Group Analysis of Differential Equations provides a systematic exposition of the theory of Lie groups and Lie algebras and its application to creating algorithms for solving the problems of the group analysis of differential equations. This text is organized into eight chapters. Chapters I to III describe the one-parameter group with its tangential field of vectors. The nonstandard treatment of the Banach Lie groups is reviewed in Chapter IV, including a discussion of the complete theory of Lie group transformations. Chapters V and VI cover the construction of partial solution classes for the given differential equation with a known admitted group. The theory of differential invariants that is developed on an infinitesimal basis is elaborated in Chapter VII. The last chapter outlines the ways in which the methods of group analysis are used in special issues involving differential equations. This publication is a good source for students and specialists concerned with areas in which ordinary and partial differential equations play an important role.
Chapter I One-Parameter Transformation Groups
1. Definitions and Examples
2. Infinitesimal Operator
3. Invariants and Invariant Manifolds
4. The Continuation Theory
Chapter II Groups Admitted by Differential Equations
5. Determining Equations
6. Group Classification Problem
7. Lie Algebra of Operators
Chapter III Full Groups of Concrete Systems of Equations
8. Ordinary Differential Equations
9. Second-Order Linear Equations with Two Independent Variables
10. Boundary Layer Equations
11. Gas Dynamics Equations
Chapter IV The Lie Theory
12. The Local Lie Group
13. The Lie Algebra
14. Associated Algebra
15. Correspondence Between Lie Groups and Lie Algebras
16. Lie Groups of Transformations
Chapter V Invariant Solutions
17. Invariants of Transformation Groups
18. Invariant Manifolds
19. Invariant Solutions of Equations
20. Classification of Invariant Solutions
Chapter VI Partial Invariance
21. Rank and Defect of Manifolds
22. Partially Invariant Solutions
23. Multiple Waves
Chapter VII Differential Invariants
24. General Theory
25. Automorphic Systems
26. Group Splitting
Chapter VIII Special Problems
27. Second-Order Linear Equations
28. Tangential Transformation
29. Boundary Value Problems
30. Conservation Laws
Appendix Tables of Calculated Full Groups
Supplementary References 404
- No. of pages:
- © Academic Press 1982
- 28th August 1982
- Academic Press
- eBook ISBN:
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