Classification of bi-Hamiltonian pairs extended by isometries. (28th July 2021)

• Record Type: Journal Article
• Authors: Pavlov, Maxim V.; Vergallo, Pierandrea; Vitolo, Raffaele
• Is Part Of: Proceedings. Volume 477:Number 2251(2021)
• Publication Date: 2021-07-28
• Subjects: Hamiltonian operators -- bi-Hamiltonian systems of PDEs -- isometries -- constant astigmatism equation; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2021.0185
• Languages: English
• ISSNs: 1364-5021

Abstract

Abstract : The aim of this article is to classify pairs of the 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 a bi-Hamiltonian pair was recently found for the constant astigmatism equation. We obtain a classification in the case of two dependent variables, and a significant new example with three dependent variables that is an extension of a hydrodynamic-type system obtained from a particular solution of the Witten–Dijkgraaf–Verlinde–Verlinde equations.