The Constrained KP Hierarchy and the Generalised Miura Transformation

Abstract

Recently much attention has been paid to the restriction of KP to the submanifold of operators which can be represented as a ratio of two purely differential operators L=AB^{-1}. Whereas most of the aspects concerning this reduced hierarchy, like the Lax flows and the Hamiltonians, are by now well understood, there still lacks a clear and conclusive statement about the associated Poisson structure. We fill this gap by placing the problem in a more general framework and then showing how the required result follows from an interesting property of the second Gelfand-Dickey brackets under multiplication and inversion of Lax operators. As a byproduct we give an elegant and simple proof of the generalised Kupershmidt-Wilson theorem.

10 pages, Plain TeX. Some statements more precisely rephrased; expanded reference list

References in corpus (8)

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Cited by in corpus (8)

• The algebra of q-pseudodifferential symbols and the q-W_{KP}^n algebra
• Constrained KP Models as Integrable Matrix Hierarchies
• Poisson Algebras associated with Constrained Dispersionless Modified KP Hierarchies
• $W_n^{(\ka)}$ algebra associated with the Moyal KdV Hierarchy
• On the Bäcklund Transformation for the Moyal Korteweg-de Vries Hierarchy
• The constrained modified KP hierarchy and the generalized Miura transformations
• On the Miura and Backlund transformations associated with the supersymmetric Gelfand-Dickey bracket
• Nonlocal extended conformal algebras associated with multi-constraint KP hierarchy and their free-field realizations