Darboux' theorem for Hamiltonian differential operators

Peter J. Olver

doi:10.1016/0022-0396(88)90036-8

Darboux' theorem for Hamiltonian differential operators

Peter J. Olver

Mathematics

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30 Scopus citations

Abstract

It is proved that any one-dimensional, first order Hamiltonian differential operator can be put into constant coefficient form by a suitable change of variables. Consequently, there exist canonical variables for any such Hamiltonian operator. In the course of the proof, a complete characterization of all first order Hamiltonian differential operators, as well as the general formula for the behavior of a Hamiltonian operator under a change of variables involving both the independent and the dependent variables are found.

Original language	English (US)
Pages (from-to)	10-33
Number of pages	24
Journal	Journal of Differential Equations
Volume	71
Issue number	1
DOIs	https://doi.org/10.1016/0022-0396(88)90036-8
State	Published - Jan 1988

Bibliographical note

Funding Information:
’ Research was supported in part by NSF Grant MCS 86-02004 and NATO Research Grant RG 86/0055.

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Darboux' theorem for Hamiltonian differential operators

Abstract

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