Characterization of partial Hamiltonian operators and related first integrals

Rehana Naz; Fazal M. Mahomed

doi:10.3934/dcdss.2018045

Article Contents

2018, Volume 11, Issue 4: 723-734. Doi: 10.3934/dcdss.2018045

This issue Previous Article Conservation laws by symmetries and adjoint symmetries Next Article New conservation forms and Lie algebras of Ermakov-Pinney equation

Characterization of partial Hamiltonian operators and related first integrals

Rehana Naz^a, and
Fazal M. Mahomed^b, ,

a.
Centre for Mathematics and Statistical Sciences, Lahore School of Economics, Lahore 53200, Pakistan
b.
DST-NRF Centre of Excellence in Mathematical and Statistical Sciences, School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, Wits 2050, South Africa

* Corresponding author: Fazal M. Mahomed
* Corresponding author: Fazal M. Mahomed

Received: October 31, 2016

Revised: March 31, 2017

Published: August 2018

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Abstract

We focus on partial Hamiltonian systems for the characterization of their operators and related first integrals. Firstly, it is shown that if an operator is a partial Hamiltonian operator which yields a first integral, then so does its evolutionary representative. Secondly, extra operator conditions are provided for a partial Hamiltonian operator in evolutionary form to yield a first integral. Thirdly, characterization of partial Hamiltonian operators and related first integral conditions are provided for the partial Hamiltonian system. Applications to mechanics are presented to illustrate the theory.

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Mathematics Subject Classification: 37K05, 70S05, 70S10.

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References

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