Group Analysis of Differential Equations

Group Analysis of Differential Equations

1st Edition - August 28, 1982

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  • Author: L. V. Ovsiannikov
  • eBook ISBN: 9781483219066

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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

Product details

  • No. of pages: 432
  • Language: English
  • Copyright: © Academic Press 1982
  • Published: August 28, 1982
  • Imprint: Academic Press
  • eBook ISBN: 9781483219066

About the Author

L. V. Ovsiannikov

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