A Poisson^Lie Framework for Rational Reductions of the KP Hierarchy
نویسنده
چکیده
We give a simple proof of I. Krichever’s theorem on rational reductions of the Kadomtsev^Petviashvili hierarchy by using the Poisson^Lie structure on the group of pseudo-differential symbols. Mathematics Subject Classi¢cations (2000). 58F07, 22E65.
منابع مشابه
Extensions of the matrix Gelfand-Dickey hierarchy from generalized Drinfeld-Sokolov reduction
The p × p matrix version of the r-KdV hierarchy has been recently treated as the reduced system arising in a Drinfeld-Sokolov type Hamiltonian symmetry reduction applied to a Poisson submanifold in the dual of the Lie algebra ĝlpr ⊗CI [λ, λ]. Here a series of extensions of this matrix Gelfand-Dickey system is derived by means of a generalized Drinfeld-Sokolov reduction defined for the Lie algeb...
متن کاملA Note on the Poisson Brackets Associated with Lax Operators
Modiications of the standard Poisson brackets associated with diierential scattering operators are considered. A linear bracket originates from a non-standard r-matrix on the algebra of pseudo-diierential operators. Two quadratic brackets are investigated which provide Hamiltonian formulations for various reductions of the modiied KP hierarchy.
متن کاملThe (N,M)–th KdV hierarchy and the associated W algebra
We discuss a differential integrable hierarchy, which we call the (N,M)–th KdV hierarchy, whose Lax operator is obtained by properly adding M pseudo–differential terms to the Lax operator of the N–th KdV hierarchy. This new hierarchy contains both the higher KdV hierarchy and multi– field representation of KP hierarchy as sub–systems and naturally appears in multi–matrix models. The N + 2M − 1 ...
متن کاملPoisson Structure of Rational Reductions of the 2D dToda Hierarchy
The paper concerns the Hamiltonian structure of the finite-dimensional reductions 2D dispersionless Toda hierarchy constrained by the string equation. We derive the Hamiltonian structure of the reduced dynamics and show connections of integrals of “multi-finger” solutions of the Laplacian growth problem with the “Toda–Krichever” flows of the 2dToda hierarchy constrained by a string equation. Th...
متن کامل0 v 2 1 7 M ay 1 99 4 KDV TYPE HIERARCHIES , THE STRING EQUATION AND W 1 + ∞ CONSTRAINTS Johan
Abstract. To every partition n = n1 + n2 + · · · + ns one can associate a vertex operator realization of the Lie algebras a∞ and ĝln. Using this construction we make reductions of the s–component KP hierarchy, reductions which are related to these partitions. In this way we obtain matrix KdV type equations. Now assuming that (1) τ is a τ–function of the [n1, n2, . . . , ns]–th reduced KP hierar...
متن کامل