DARBOUX-BACKLUND SOLUTIONS OF SL(P,Q) KP-KDV HIERARCHIES, CONSTRAINED GENERALIZED TODA-LATTICES, AND 2-MATRIX STRING MODEL

We present a unifying description of the graded SL(p, q) KP-KdV hierarchies, including the Wronskian construction of their tau-functions as well as the coefficients of the pertinent Lax operators, obtained via successive applications of special Darboux-Backlund transformations. The emerging Darboux-Backlund structure is identified as a constrained generalized Toda lattice system relevant for the two-matrix string model, It allows simple derivation of the eta-soliton solutions of the unconstrained KP system, Also, the exact Wronskian solution for the two-matrix model partition function is found.