Additional symmetries of the KP-mKP hierarchy and Virasoro constraints to the Burgers-KdV hierarchy

2026/03/02 by Zongyao Feng, Lumin Geng, Chao-Zhong Wu · 1 voice
Physics and Astronomy · #nlin.SI

paper · pdf · doi:10.1007/s11005-026-02104-5

arxiv published 2026/03/02 · arxiv updated 2026/06/22

Abstract

A KP-mKP hierarchy was introduced recently via pseudo-differential operators containing two derivations. In this paper, for the KP-mKP hierarchy we derive a class of (differential) Fay identities and construct a series of additional symmetries. Moreover, the additional symmetries are represented as certain linear actions on the tau functions of the hierarchy, with the help of the Adler-Shiota-van Moerbeke formula. As an application, we reprove the Virasoro constraints to the tau functions of the Burgers-KdV hierarchy, and such results are generalized to its higher order extensions regarded as reductions of the KP-mKP hierarchy.

Citations

• Reduction properties of the KP-mKP hierarchy
• Bilinear equation and additional symmetries for an extension of the Kadomtsev-Petviashvili hierarchy
• Equivalence of formulations of the MKP hierarchy and its polynomial tau-functions
• Additional symmetries of the extended bigraded Toda hierarchy
• An extension of the Kadomtsev–Petviashvili hierarchy and its hamiltonian structures
• The partition function of the extended r-reduced Kadomtsev-Petviashvili hierarchy
• Open intersection numbers, matrix models and MKP hierarchy
• Open intersection numbers and the wave function of the KdV hierarchy
• Equivalence of the open KdV and the open Virasoro equations for the moduli space of Riemann surfaces with boundary
• From Additional Symmetries to Linearization of Virasoro Symmetries
• Dispersionful analogue of the Whitham hierarchy
• The spectrum of coupled random matrices
• Virasoro Symmetry of Constrained KP Hierarchies
• On additional symmetries of the KP hierarchy and Sato's Bäcklund transformation
• Solitons and Infinite Dimensional Lie Algebras

Discussions

• Zongyao Feng, Lumin Geng, Chao-Zhong Wu: Additional symmetries of the KP-mKP hierarchy and Virasoro constraints to the Burgers-KdV hierarchy https://arxiv.org/abs/2603.01354 https://arxiv.org/pdf/2603 [bsky, 0 points, 0 comments]

Related

• Tau function of the CKP hierarchy and non-linearizable Virasoro symmetries
• Bilinear equation and additional symmetries for an extension of the Kadomtsev-Petviashvili hierarchy
• A KP-mKP Hierarchy via Operators with Two Derivations
• Equivalence of formulations of the MKP hierarchy and its polynomial tau-functions
• Squared eigenfunction symmetry of the DΔmKP hierarchy and its constraint