Elements of Superintegrable Systems

Basic Techniques and Results

  • B. A. Kupershmidt

Part of the Mathematics and Its Applications book series (MAIA, volume 34)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Classical Superintegrable Systems

  3. Lie Algebras, Korteweg-De Vries Equations, and Bi-Superhamiltonian Systems

    1. Front Matter
      Pages 99-99
    2. B. A. Kupershmidt
      Pages 101-137
    3. B. A. Kupershmidt
      Pages 138-157
    4. B. A. Kupershmidt
      Pages 158-173
  4. Back Matter
    Pages 174-187

About this book


Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day. that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hennit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.


algebraic geometry chaos derivative filtering geometry hamiltonian system integrable system measure measure theory pseudodifferential operator residue synergetics variational calculus variational problem

Authors and affiliations

  • B. A. Kupershmidt
    • 1
  1. 1.The University of Tennessee Space InstituteTullahomaUSA

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media B.V. 1987
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-010-8190-0
  • Online ISBN 978-94-009-3799-4
  • Buy this book on publisher's site
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