Weakly nonlocal Poisson brackets, Schouten brackets and supermanifolds
Mathematical Physics
2021-12-21 v2 math.MP
Exactly Solvable and Integrable Systems
Abstract
Poisson brackets between conserved quantities are a fundamental tool in the theory of integrable systems. The subclass of weakly nonlocal Poisson brackets occurs in many significant integrable systems. Proving that a weakly nonlocal differential operator defines a Poisson bracket can be challenging. We propose a computational approach to this problem through the identification of such operators with superfunctions on supermanifolds.
Keywords
Cite
@article{arxiv.1909.07695,
title = {Weakly nonlocal Poisson brackets, Schouten brackets and supermanifolds},
author = {P. Lorenzoni and R. Vitolo},
journal= {arXiv preprint arXiv:1909.07695},
year = {2021}
}
Comments
Added a dedication to J.S. Krasilshchik for his 70th birthday. 15 pages, misprint corrected