Virasoro symmetry of the constrained multi-component KP hierarchy and its integrable discretization

TL;DR

This paper constructs Virasoro symmetries for a constrained multi-component KP hierarchy, demonstrates their algebraic structure, and shows this structure persists after discretization, advancing understanding of integrable systems.

Contribution

It introduces Virasoro symmetries for the constrained multi-component KP hierarchy and proves their algebraic structure remains intact under discretization.

Findings

Virasoro symmetries are constructed for the hierarchy.

The algebraic structure of Virasoro symmetry is preserved after discretization.

Virasoro flow equations are formulated for eigenfunctions and adjoint eigenfunctions.

Abstract

In this paper, we construct the Virasoro type additional symmetries of a kind of constrained multi-component KP hierarchy and give the Virasoro flow equation on eigenfunctions and adjoint eigenfunctions. It can also be seen that the algebraic structure of the Virasoro symmetry is kept after discretization from the constrained multi-component KP hierarchy to the discrete constrained multi-component KP hierarchy.