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-Bäcklund transformations. The emerging Darboux-Bäcklund 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.

LaTeX, 13 pgs, minor typos corrected (incl. in eq. (90))

References in corpus (6)

• R-Matrix Formulation of KP Hierarchies and their Gauge Equivalence
• Multi-field representations of KP hierarchies and multi-matrix models
• Construction of KP Hierarchies in Terms of Finite Number of Fields and their Abelianization
• Many Boson Realizations of Universal Nonlinear $W_{\infty }$-Algebras
• Two-Matrix String Model as Constrained (2+1)-Dimensional Integrable System
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• Constrained KP Models as Integrable Matrix Hierarchies
• Tau-Functions generating the Conservation Laws for Generalized Integrable Hierarchies of KdV and Affine-Toda type
• Manifestly Supersymmetric Lax Integrable Hierarchies
• Solitons from Dressing in an Algebraic Approach to the Constrained KP Hierarchy
• The N=2 Supersymmetric Heavenly Equation and Its Super-Hydrodynamical Reduction