Hamiltonian Structures of the Multi-Boson KP Hierarchies, Abelianization and Lattice Formulation

Abstract

We present a new form of the multi-boson reduction of KP hierarchy with Lax operator written in terms of boson fields abelianizing the second Hamiltonian structure. This extends the classical Miura transformation and the Kupershmidt-Wilson theorem from the (m)KdV to the KP case. A remarkable relationship is uncovered between the higher Hamiltonian structures and the corresponding Miura transformations of KP hierarchy, on one hand, and the discrete integrable models living on {\em refinements} of the original lattice connected with the underlying multi-matrix models, on the other hand. For the second KP Hamiltonian structure, worked out in details, this amounts to finding a series of representations of the nonlinear $\hWinf$ algebra in terms of arbitrary finite number of canonical pairs of free fields.

12 pgs, (changes in abstract, intro and outlook+1 ref added). LaTeX, BGU-94 / 1 / January- PH, UICHEP-TH/94-2

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• Constrained KP Models as Integrable Matrix Hierarchies
• Two-Matrix String Model as Constrained (2+1)-Dimensional Integrable System
• Symmetries of Supersymmetric Integrable Hierarchies of KP Type
• A Symmetric System of Mixed Painleve III - V Equations and its Integrable Origin