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Applications of Lie Groups to Differential Equations

  • Textbook
  • © 1993

Overview

Authors:
  1. Peter J. Olver

    1. School of Mathematics, University of Minnesota, Minneapolis, USA

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Part of the book series: Graduate Texts in Mathematics (GTM, volume 107)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xxviii
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  2. Introduction to Lie Groups

    • Peter J. Olver
    Pages 1-74

  3. Symmetry Groups of Differential Equations

    • Peter J. Olver
    Pages 75-182

  4. Group-Invariant Solutions

    • Peter J. Olver
    Pages 183-241

  5. Symmetry Groups and Conservation Laws

    • Peter J. Olver
    Pages 242-285

  6. Generalized Symmetries

    • Peter J. Olver
    Pages 286-388

  7. Finite-Dimensional Hamiltonian Systems

    • Peter J. Olver
    Pages 389-432

  8. Hamiltonian Methods for Evolution Equations

    • Peter J. Olver
    Pages 433-466

  9. Back Matter

    Pages 467-516
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Keywords

About this book

Symmetry methods have long been recognized to be of great importance for the study of the differential equations. This book provides a solid introduction to those applications of Lie groups to differential equations which have proved to be useful in practice. The computational methods are presented so that graduate students and researchers can readily learn to use them. Following an exposition of the applications, the book develops the underlying theory. Many of the topics are presented in a novel way, with an emphasis on explicit examples and computations. Further examples, as well as new theoretical developments, appear in the exercises at the end of each chapter.

Authors and Affiliations

  • School of Mathematics, University of Minnesota, Minneapolis, USA

    Peter J. Olver

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