Anisotropic inharmonic Higgs oscillator and related (MICZ-)Kepler-like systems

TL;DR

This paper introduces a new integrable generalization of the anisotropic oscillator and MICZ-Kepler systems on (pseudo)spherical geometries, including coordinate separability and spherical analogs.

Contribution

It presents the first (pseudo)spherical generalization of the anisotropic oscillator and MICZ-Kepler systems, with new coordinate systems and separability properties.

Findings

Derived the (pseudo)spherical MICZ-Kepler generalization with potential terms.

Established separation of variables in generalized coordinates.

Constructed the spherical analog of the MICZ-Kepler-like system.

Abstract

We propose the integrable (pseudo)spherical generalization of the four-dimensional anisotropic oscillator with additional nonlinear potential. Performing its Kustaanheimo-Stiefel transformation we then obtain the pseudospherical generalization of the MICZ-Kepler system with linear and $\cos\theta$ potential terms. We also present the generalization of the parabolic coordinates, in which this system admits the separation of variables. Finally, we get the spherical analog of the presented MICZ-Kepler-like system.