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Group Analysis of Differential Equations
1st Edition - August 28, 1982
Author: L. V. Ovsiannikov
eBook ISBN:
9 7 8 - 1 - 4 8 3 2 - 1 9 0 6 - 6
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… Read more
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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.
Editor's PrefacePrefaceNotationChapter I One-Parameter Transformation Groups 1. Definitions and Examples 2. Infinitesimal Operator 3. Invariants and Invariant Manifolds 4. The Continuation Theory ReferencesChapter II Groups Admitted by Differential Equations 5. Determining Equations 6. Group Classification Problem 7. Lie Algebra of Operators ReferencesChapter 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 ReferencesChapter 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 ReferencesChapter V Invariant Solutions 17. Invariants of Transformation Groups 18. Invariant Manifolds 19. Invariant Solutions of Equations 20. Classification of Invariant Solutions ReferencesChapter VI Partial Invariance 21. Rank and Defect of Manifolds 22. Partially Invariant Solutions 23. Multiple Waves ReferencesChapter VII Differential Invariants 24. General Theory 25. Automorphic Systems 26. Group Splitting ReferencesChapter VIII Special Problems 27. Second-Order Linear Equations 28. Tangential Transformation 29. Boundary Value Problems 30. Conservation Laws ReferencesAppendix Tables of Calculated Full GroupsSupplementary References 404Index
- No. of pages: 432
- Language: English
- Published: August 28, 1982
- Imprint: Academic Press
- eBook ISBN: 9781483219066