2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153455We 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.19 pages, AMSLATEXQuantum AlgebraHigh Energy Physics - Theorytext