2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149108Perturbations of $WD_n$ and $W_3$ conformal theories which generalize the $(1,2)$ perturbations of conformal minimal models are shown to be integrable by counting argument. $A_{2n-1,q}^{(2)}$ and $D_{4,q}^ {(3)}$ symmetries of corresponding S-matrices are conjectured and proved by explicit construction of conserved nonlocal charges in the $WD_3$ case with the proper quantum group of symmetry.Latex file. 18 pages. (Final part was changed)High Energy Physics - Theorytext