Applications of Lie Groups to Differential Equations

  • Peter J. Olver

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

Table of contents

  1. Front Matter
    Pages i-xxvi
  2. Peter J. Olver
    Pages 1-76
  3. Peter J. Olver
    Pages 77-185
  4. Peter J. Olver
    Pages 186-245
  5. Peter J. Olver
    Pages 246-291
  6. Peter J. Olver
    Pages 292-377
  7. Peter J. Olver
    Pages 378-422
  8. Peter J. Olver
    Pages 423-474
  9. Back Matter
    Pages 457-500

About this book

Introduction

This book is devoted to explaining a wide range of applications of con­ tinuous symmetry groups to physically important systems of differential equations. Emphasis is placed on significant applications of group-theoretic methods, organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems. The first chapter collects together (but does not prove) those aspects of Lie group theory which are of importance to differential equations. Applications covered in the body of the book include calculation of symmetry groups of differential equations, integration of ordinary differential equations, including special techniques for Euler-Lagrange equations or Hamiltonian systems, differential invariants and construction of equations with pre­ scribed symmetry groups, group-invariant solutions of partial differential equations, dimensional analysis, and the connections between conservation laws and symmetry groups. Generalizations of the basic symmetry group concept, and applications to conservation laws, integrability conditions, completely integrable systems and soliton equations, and bi-Hamiltonian systems are covered in detail. The exposition is reasonably self-contained, and supplemented by numerous examples of direct physical importance, chosen from classical mechanics, fluid mechanics, elasticity and other applied areas.

Keywords

Applications Equations Groups Lie group theory

Authors and affiliations

  • Peter J. Olver
    • 1
  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-0274-2
  • Copyright Information Springer-Verlag New York 1986
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4684-0276-6
  • Online ISBN 978-1-4684-0274-2
  • Series Print ISSN 0072-5285
  • About this book