Darboux-Backlund Solutions of SL(p,q) KP-KdV Hierarchies, Constrained Generalized Toda Lattices, and Two-Matrix String Model
Abstract
We present an 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-B\"acklund transformations. The emerging Darboux-B\"acklund structure is identified as a constrained generalized Toda lattice system relevant for the two-matrix string model. Also, the exact Wronskian solution for the two-matrix model partition function is found.
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