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Integrability pp 139-173 | Cite as

Symmetries of Spectral Problems

  • A. Shabat
Part of the Lecture Notes in Physics book series (LNP, volume 767)

Abstract

Deriving abelian KdV and NLS hierarchies, we describe non-abelian symmetries and “pre-Lax” elementary approach to Lax pairs. Discrete symmetries of spectral problems are considered in Sect. 4.2. Here we prove Darboux classical theorem and discuss a modern theory of dressing chains.

Keywords

Riccati Equation Spectral Problem Discrete Symmetry Darboux Transformation Transformation Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • A. Shabat
    • 1
  1. 1.L.D. Landau Institute for Theoretical PhysicsRussia

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