Classification of bi-Hamiltonian pairs extended by isometries-Reference-Cited by-同舟云学术

Classification of bi-Hamiltonian pairs extended by isometries

Published:2021-07 Issue:2251 Volume:477 Page:20210185
ISSN:1364-5021
Container-title:Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Proc. R. Soc. A.

Author:

Pavlov Maxim V.¹,Vergallo Pierandrea²³,Vitolo Raffaele²³^ORCID

Affiliation:

1. Department of Mathematical Physics, Lebedev Physical Institute of Russian Academy of Sciences, Leninskij Prospekt 53, Moscow, Russia

2. Department of Mathematics and Physics ‘E. De Giorgi’, University of Salento, Lecce, Italy

3. INFN, Section of Lecce, Italy

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.

Funder

RFBR

Istituto Nazionale di Fisica Nucleare

Università del Salento

Istituto Nazionale di Alta Matematica “Francesco Severi”

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2021.0185

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