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.
Lorenzoni, P., Vitolo, R. (2020). Weakly nonlocal Poisson brackets, Schouten brackets and supermanifolds. JOURNAL OF GEOMETRY AND PHYSICS, 149 [10.1016/j.geomphys.2019.103573].
Weakly nonlocal Poisson brackets, Schouten brackets and supermanifolds
Lorenzoni P.
;
2020
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.
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