Weakly nonlocal Poisson brackets, Schouten brackets and supermanifolds
arXiv:1909.07695 · doi:10.1016/j.geomphys.2019.103573
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.
Added a dedication to J.S. Krasilshchik for his 70th birthday. 15 pages, misprint corrected