On the String Equation of the BKP Hierarchy

TL;DR

This paper derives W-constraints for the p-reduced BKP hierarchy constrained by the string equation using the Adler-Shiota-van Moerbeke formula and describes it via Grassmannian in spectral parameter terms.

Contribution

It introduces a novel derivation of W-constraints for the p-reduced BKP hierarchy with string equation constraints and offers a Grassmannian perspective.

Findings

Derived W-constraints for the p-reduced BKP hierarchy

Provided Grassmannian description in spectral parameter

Connected string equation with integrable hierarchy constraints

Abstract

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 spectral parameter.