  Let KdV stand for the Nth Gelfand-Dickey reduction of the KP hierarchy. The
purpose of this paper is to show that any KdV solution leads effectively to a
solution of the q-approximation of KdV. Two different q-KdV approximations were
proposed, one by Frenkel and a variation by Khesin et al. We show there is a
dictionary between the solutions of q-KP and the 1-Toda lattice equations,
obeying some special requirement; this is based on an algebra isomorphism
between difference operators and D-operators, where $Df(x)=f(qx)$. Therefore,
every notion about the 1-Toda lattice can be transcribed into q-language.
