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arXiv · 2011.04073

Classification of bi-Hamiltonian pairs extended by isometries

Maxim V. Pavlov·Pierandrea Vergallo·Raffaele Vitolo
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Abstract

The aim of this article is to classify pairs of first-order Hamiltonian operators of Dubrovin-Novikov type such that one of them has a non-local part defined by an isometry of its leading coefficient. An example of such bi-Hamiltonian pair was recently found for the constant astigmatism equation. We obtain a classification in the case of 2 dependent variables, and a significant new example that is an extension of a hydrodynamic type system obtained from a particular solution of the WDVV equations.

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Maxim V. Pavlov, Pierandrea Vergallo, Raffaele Vitolo. 2020-11-08. Classification of bi-Hamiltonian pairs extended by isometries. https://doi.org/10.1098/rspa.2021.0185

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