Group Analysis of Differential Equations and Integrable Systems − 2018
Allan Fordy (University of Leeds, UK)
First integrals from conformal symmetries: Darboux-Koenigs metrics and beyond
In this talk we use these conformal symmetries to build higher order integrals for the geodesic equations. We use this approach to give a new derivation of the Darboux-Koenigs metrics, which have only one Killing vector, but two quadratic integrals. We also consider the case of possessing one Killing vector and two cubic integrals.
The approach allows the quantum analogue to be constructed in a simpler manner.
Based on: arXiv:1804.06904 [nlin.SI].