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Nonlinear Symmetries and Nonlinear Equations

  • Giuseppe Gaeta

Part of the Mathematics and Its Applications book series (MAIA, volume 299)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Giuseppe Gaeta
    Pages 1-22
  3. Giuseppe Gaeta
    Pages 23-44
  4. Giuseppe Gaeta
    Pages 45-54
  5. Giuseppe Gaeta
    Pages 55-82
  6. Giuseppe Gaeta
    Pages 83-95
  7. Giuseppe Gaeta
    Pages 97-121
  8. Giuseppe Gaeta
    Pages 123-154
  9. Giuseppe Gaeta
    Pages 155-173
  10. Giuseppe Gaeta
    Pages 175-204
  11. Giuseppe Gaeta
    Pages 205-222
  12. Back Matter
    Pages 223-260

About this book

Introduction

The study of (nonlinear) dift"erential equations was S. Lie's motivation when he created what is now known as Lie groups and Lie algebras; nevertheless, although Lie group and algebra theory flourished and was applied to a number of dift"erent physical situations -up to the point that a lot, if not most, of current fun­ damental elementary particles physics is actually (physical interpretation of) group theory -the application of symmetry methods to dift"erential equations remained a sleeping beauty for many, many years. The main reason for this lies probably in a fact that is quite clear to any beginner in the field. Namely, the formidable comple:rity ofthe (algebraic, not numerical!) computations involved in Lie method. I think this does not account completely for this oblivion: in other fields of Physics very hard analytical computations have been worked through; anyway, one easily understands that systems of dOlens of coupled PDEs do not seem very attractive, nor a very practical computational tool.

Keywords

bifurcation differential equation dynamical systems geometry mathematical physics

Authors and affiliations

  • Giuseppe Gaeta
    • 1
  1. 1.Centre de Physique ThéoriqueEcole PolytechniquePalaiseauFrance

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