Deformations of the KdV hierarchy and related soliton equations

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.

arXiv comment19 pages, AMSLATEX

Cited by in corpus (7)

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• q-Deformed KP Hierarchy and q-Deformed Constrained KP Hierarchy
• Classical R-matrix theory for bi-Hamiltonian field systems
• Sato theory on the $q$-Toda hierarchy and its extension
• Virasoro and W-constraints for the $q$-KP hierarchy
• Cubic Hodge integrals and integrable hierarchies of Volterra type
• Integrable Equations on Time Scales