The partition function of the extended $r$-reduced Kadomtsev-Petviashvili hierarchy

Abstract

We derive a particular solution of the extended $r$-reduced KP hierarchy, which is specified by a generalized string equation. The work is a generalization to arbitrary $r\ge 2$ of Buryak's recent results of a solution to the extended open KdV hierarchy which corresponds to $r=2$.

arXiv comment18 pages

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Cited by in corpus (16)

• Correlation functions of the KdV hierarchy and applications to intersection numbers over ${\overline{\mathcal{M}}}_{g,n}$
• Open intersection numbers, Kontsevich-Penner model and cut-and-join operators
• Higher Airy structures and topological recursion for singular spectral curves
• Open intersection numbers and the wave function of the KdV hierarchy
• Higher Airy structures, W algebras and topological recursion
• Simple Lie algebras, Drinfeld--Sokolov hierarchies, and multi-point correlation functions
• Genus expansion of open free energy in 2d topological gravity
• Minimal gravity and Frobenius manifolds: bulk correlation on sphere and disk
• From minimal gravity to open intersection theory
• On an extension of the generalized BGW tau-function
• Geometry and arithmetic of integrable hierarchies of KdV type. I. Integrality
• On tau-functions for the KdV hierarchy
• Closed extended $r$-spin theory and the Gelfand-Dickey wave function
• d-orthogonal polynomials, Toda Lattice and Virasoro symmetries
• Topological Two-Dimensional Gravity on Surfaces with Boundary
• On affine coordinates of the tau-function for open intersection numbers