Group Analysis of Differential Equations - 1st Edition - ISBN: 9780125316804, 9781483219066

Group Analysis of Differential Equations

1st Edition

Authors: L. V. Ovsiannikov
eBook ISBN: 9781483219066
Imprint: Academic Press
Published Date: 28th August 1982
Page Count: 432
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Description

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.

Table of Contents


Editor's Preface

Preface

Notation

Chapter I One-Parameter Transformation Groups

1. Definitions and Examples

2. Infinitesimal Operator

3. Invariants and Invariant Manifolds

4. The Continuation Theory

References

Chapter II Groups Admitted by Differential Equations

5. Determining Equations

6. Group Classification Problem

7. Lie Algebra of Operators

References

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

References

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

References

Chapter V Invariant Solutions

17. Invariants of Transformation Groups

18. Invariant Manifolds

19. Invariant Solutions of Equations

20. Classification of Invariant Solutions

References

Chapter VI Partial Invariance

21. Rank and Defect of Manifolds

22. Partially Invariant Solutions

23. Multiple Waves

References

Chapter VII Differential Invariants

24. General Theory

25. Automorphic Systems

26. Group Splitting

References

Chapter VIII Special Problems

27. Second-Order Linear Equations

28. Tangential Transformation

29. Boundary Value Problems

30. Conservation Laws

References

Appendix Tables of Calculated Full Groups

Supplementary References 404

Index

Details

No. of pages:
432
Language:
English
Copyright:
© Academic Press 1982
Published:
Imprint:
Academic Press
eBook ISBN:
9781483219066

About the Author

L. V. Ovsiannikov