相关论文: The Constrained MKP Hierarchy and the Generalized …
We show how the relation between Poisson brackets and symplectic forms can be extended to the case of inhomogeneous multivector fields and inhomogeneous differential forms (or pseudodifferential forms). In particular we arrive at a notion…
Restricting a linear system for the KP hierarchy to those independent variables t\_n with odd n, its compatibility (Zakharov-Shabat conditions) leads to the "odd KP hierarchy". The latter consists of pairs of equations for two dependent…
Following Natanzon-Zabrodin, we explore the Kadomtsev-Petviashvili hierarchy as an infinite system of mutually consistent relations on the second derivatives of the free energy with some universal coefficients. From this point of view,…
In the study of alternative or extended theories of gravity, Dirac's Hamiltonian constraint algorithm is invaluable for enumerating the propagating modes and gauge symmetries. For gravity, this canonical approach is frequently applied as a…
Motivated by the phenomenon that compatible Poisson structures on a cluster algebra play a key role on its quantization (that is, quantum cluster algebra), we introduce the second quantization of a quantum cluster algebra, which means the…
Modified Toda hierarchy is a two-component generalization of the 1st modified KP hierarchy, which has been widely applied to analyze constraints of the Toda hierarchy, including the B--Toda and C--Toda hierarchies. In this paper, we…
A covariant pseudodifferential calculus on Riemann surfaces, based on the Krichever-Novikov global picture, is presented. It allows defining scalar and matrix KP operators, together with their reductions, in higher genus. Globally defined…
We illustrate the basic notions of {\em additional non-isospectral symmetries} and their interplay with the discrete {\em \DB transformations} of integrable systems at the instance of {\em constrained Kadomtsev-Petviashvili} (\cKP)…
We discuss dimensional reduction for Hamiltonian systems which possess nonconstant Poisson brackets between pairs of coordinates and between pairs of momenta. The associated Jacobi identities imply that the dimensionally reduced brackets…
The constrained structure of the duality invariant form of Maxwell theory is considered in the Hamiltonian formulation of Dirac as well as from the symplectic viewpoint. Compared to the former the latter approach is found to be more…
We introduce a natural class of multicomponent local Poisson structures $\mathcal P_k + \mathcal P_1$, where $\mathcal P_1$ is a local Poisson bracket of order one and $\mathcal P_k$ is a homogeneous Poisson bracket of odd order $k$ under…
We generalize to the supersymmetric case the representation of the KP hierarchy as a set of conservation laws for the generating series of the conserved densities. We show that the hierarchy so obtained is isomorphic to the JSKP of Mulase…
It is shown how derived brackets naturally arise in sigma-models via Poisson- or antibracket, generalizing a recent observation by Alekseev and Strobl. On the way to a precise formulation of this relation, an explicit coordinate expression…
We construct a new multi-component CKP hierarchy based on the eigenfunction symmetry reduction. It contains two types of CKP equation with self-consistent sources which Lax representations are presented. Also it admits reductions to…
We show directly in the Lax operator approach how the Virasoro and W-constraints on the $\tau$-function arise in the $p$-reduced KP hierarchy or generalized KdV hierarchy. In partiacular, we consider the KdV and Boussinesq hierarchy to show…
The Adler-Shiota-van Moerbeke formula is employed to derive the $W$-constraints for the $p$-reduced BKP hierarchy constrained by the string equation. We also provide the Grassmannian description of the string equation in terms of the…
A Keller map is a counterexample to the Jacobian Conjecture. In dimension two every such map, if exists, leads to a complicated set of conditions on the map between the Picard groups of suitable compactifications of the affine plane. This…
We consider the extended discrete KP hierarchy and show that similarity reduction of its subhierarchies lead to purely discrete equations with dependence on some number of parameters together with equations governing deformations with…
The coupled KP hierarchy, introduced by Hirota and Ohta, are investigated by using the dressing method. It is shown that the coupled KP hierarchy can be reformulated as a reduced case of the 2-component KP hierarchy.
We introduce a notion of noncommutative Poisson-Nijenhuis structure on the path algebra of a quiver. In particular, we focus on the case when the Poisson bracket arises from a noncommutative symplectic form. The formalism is then applied to…