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Deformations of the KdV hierarchy and related soliton equations

Edward Frenkel
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Abstract

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 sl(N), defined by Reshetikhin and the author. We also find q-deformations of the mKdV hierarchies and the affine Toda equations.

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Edward Frenkel. 1995-11-06. Deformations of the KdV hierarchy and related soliton equations. https://arxiv.org/abs/q-alg/9511003

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