Hamiltonian differential operators and contact geometry
type: Item
instance of: scholarly article
title: Hamiltonian differential operators and contact geometry
zbMATH Open document ID: 0635.58006
DOI: 10.1007/BF02577136
publication date: 1987-01-01T00:00:00Z
review text: The problem of classification of Hamiltonian differential operators is investigated. An operator (1) \(L=\sum^{N}_{i=0}a_ i(x,u,u_ x,...)(\frac{d}{dx})^ i\) is called the Hamiltonian if the formula \[ \{I,J\}=\int (\delta I/\delta u)L(\delta J/\delta u)dx \] defines a Poisson bracket on the space of all functionals \(H=\int h(x,u,u_ x,...)dx\). The purpose of the paper is to get some Darboux-type results to classify Hamiltonian operators of the first and the third order under contact Bäcklund transformations. The notion of a Hamiltonian pair of operators, i.e. \(L_ 1,L_ 2\) of the form (1), such that \(\lambda L_ 1+\mu L_ 2\) is a Hamiltonian operator for any \(\lambda\),\(\mu\in {\mathbb{R}}\), is very important in the theory of integrability of evolution equations. The author studies the problem of classification of such pairs, consisting of \(L_ 1\) having first order and \(L_ 2\) having third order.
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 58D05
zbMATH DE Number: 4034695
zbMATH Keywords: classification under contact transformations
zbMATH Keywords: Hamiltonian differential operators
zbMATH Keywords: Bäcklund transformations
author: O. I. Mokhov
MaRDI profile type: Publication
Wikidata QID: Q115391959
cites work: Q3865176
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published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 4034695