String Equations of the q-KP Hierarchy

TL;DR

This paper derives string equations for the q-KP hierarchy using Lax and Orlov-Shulman operators, and identifies Virasoro constraints for the 2-reduced case, advancing understanding of integrable systems.

Contribution

It introduces a method to establish string equations for the q-KP hierarchy and derives Virasoro constraints for the 2-reduced hierarchy, a novel approach in this area.

Findings

String equations derived from special symmetry flows.

Negative Virasoro constraints obtained for the 2-reduced hierarchy.

Enhanced understanding of the algebraic structure of q-KP systems.

Abstract

Based on the Lax operator $L$ and Orlov-Shulman's $M$ operator, the string equations of the $q$-KP hierarchy are established from special additional symmetry flows, and the negative Virasoro constraint generators \{$L_{-n}, n\geq1$\} of the $2-$reduced $q$-KP hierarchy are also obtained.