Graduate Texts in Mathematics

Applications of Lie Groups to Differential Equations

Authors: Olver, Peter J.

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About this Textbook

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.

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $74.99
price for USA in USD (gross)
  • ISBN 978-1-4684-0274-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Applications of Lie Groups to Differential Equations
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
107
Copyright
1986
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York Inc.
eBook ISBN
978-1-4684-0274-2
DOI
10.1007/978-1-4684-0274-2
Series ISSN
0072-5285
Edition Number
1
Topics