Integrability pp 139-173 | Cite as

Symmetries of Spectral Problems

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


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.


Riccati Equation Spectral Problem Discrete Symmetry Darboux Transformation Transformation Operator 
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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

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

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