The Adler-Shiota-van Moerbeke formula for the BKP hierarchy
Johan van de Leur
TL;DR
This paper establishes an Adler-Shiota-van Moerbeke formula for the BKP hierarchy, linking algebraic actions on tau-functions to symmetries on wave functions, advancing understanding of integrable systems.
Contribution
It proves the existence of a new formula connecting algebraic and symmetry actions in the BKP hierarchy, a significant theoretical development.
Findings
Established the Adler-Shiota-van Moerbeke formula for BKP hierarchy
Connected $BW_{1+ infty}$ algebra actions to additional symmetries
Enhanced understanding of symmetry structures in integrable systems
Abstract
We study the BKP hierarchy and prove the existence of an Adler--Shiota--van Moerbeke formula. This formula relates the action of the --algebra on tau--functions to the action of the ``additional symmetries'' on wave functions.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons