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arXiv · 1909.07695

Weakly nonlocal Poisson brackets, Schouten brackets and supermanifolds

P. Lorenzoni·R. Vitolo
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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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P. Lorenzoni, R. Vitolo. 2019-09-17. Weakly nonlocal Poisson brackets, Schouten brackets and supermanifolds. https://doi.org/10.1016/j.geomphys.2019.103573

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