Conclusion

  • Ludwig D. Faddeev
  • Leon A. Takhtajan
Part of the Springer Series in Soviet Mathematics book series (CLASSICS)

Abstract

This conclusion is intended for those who have read the book to the end. We hope that the main text and the notes to separate chapters have furnished a convincing evidence of how rich from the mathematical point of view, both conceptually and technically, is the subject of solitons and integrable partial differential equations. In fact, the inverse scattering method naturally intertwines various branches of mathematics: differential geometry, the theory of Lie groups and Lie algebras and their representations, complex and functional analysis. All of them serve one common purpose, to classify integrable equations and describe their solutions. As a result, the traditional parts of these branches, such as Hamiltonian formalism, affine Lie algebras, or the Riemann problem are seen in a new light.

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Ludwig D. Faddeev
    • 1
  • Leon A. Takhtajan
    • 1
  1. 1.Steklov Mathematical InstituteLeningradUSSR

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