A Coset-Construction for Integrable Hierarchies

  • F. Alexander Bais
  • Koos de Vos
Part of the NATO ASI Series book series (NSSB, volume 245)


The principal realization of the basic representation of an affine Kac-Moody algebra can be applied to construct soliton solutions of hierarchies of partial differential equations, among them the KdV- and KP-equations.

In this construction, called orbit-construction, the equations of the hierarchy itself arise in Hirota bilinear form. Using the Goddard-Kent-Olive coset-construction of conformai field theory, we show that the equations are generated by a pair of commuting c=1/2 Virasoro algebras in the KdV-case. We end with a brief discussion of other cases.


Tensor Product Soliton Solution Conformal Field Theory Classical Hierarchy High Weight Vector 
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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • F. Alexander Bais
    • 1
  • Koos de Vos
    • 1
  1. 1.Institute for Theoretical PhysicsUniversity of AmsterdamAmsterdamThe Netherlands

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