Deformations of the Kdv Hierarchy and Related Soliton Equations

  title={Deformations of the Kdv Hierarchy and Related Soliton Equations},
  author={Edward Frenkel},
We define hierarchies of differential–q-difference equations, which are q–deformations of the equations of the generalized KdV hierarchies. We show that these hierarchies are bihamiltonian, one of the hamiltonian structures being that of the q–deformed classical W–algebra of slN , defined by Reshetikhin and the author. We also find q–deformations of the mKdV hierarchies and the affine Toda equations. 
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