  We propose an alternative description of 2 dimensional Conformal Field Theory
in terms of Quantum Inverse Scattering. It is based on the generalized KdV
systems attached to $A_2^{(2)}$, yielding the classical limit of Virasoro as
Poisson bracket structure. The corresponding T-system is shown to coincide with
the one recently proposed by Kuniba and Suzuki. We classify the primary
operators of the minimal models that commute with all the Integrals of Motion,
and that are therefore candidates to perturb the model by keeping the
conservation laws. For our $A_2^{(2)}$ structure these happen to be
$\phi_{1,2},\phi_{2,1},\phi_{1,5}$, in contrast to the $A_1^{(1)}$ case,
studied by Bazhanov, Lukyanov and Zamolodchikov~\cite{BLZ}, related to
$\phi_{1,3}$.
