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In the spirit of the quantum Hamiltonian reduction we establish a relation between the chiral n-point functions, as well as the equations governing them, of the A (1) 1 WZNW conformal theory and the corresponding Virasoro minimal models. The WZNW correlators are described as solutions of the Knizhnik -Zamolodchikov equations with rational levels and isospins. The technical tool exploited are certain relations in twisted cohomology. The results extend to arbitrary level k + 2 = 0 and isospin values of the type J = j − j ′ (k + 2), 2j, 2j ′ ∈ Z Z + .

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We present an elementary derivation of the soliton-like solutions in the A (1) n Toda models which is alternative to the previously used Hirota method. The solutions of the underlying linear problem corresponding to the N -solitons are calculated. This enables us to obtain explicit expression for the element which by dressing group action, produces a generic soliton solution. In the particular example of monosolitons we suggest a relation to the vertex operator formalism, previously used by Olive, Turok and Underwood. Our results can also be considered as generalization of the approach to the sine-Gordon solitons, proposed