On the Ermakov systems and nonlocal symmetries

TL;DR

This paper identifies new nonlocal symmetries in three classes of Ermakov systems using an algebraic reduction method, expanding the understanding of their symmetry properties.

Contribution

The paper introduces novel nonlocal symmetries for Ermakov systems through a straightforward algebraic reduction, which were not previously documented.

Findings

Discovered new nonlocal symmetries for three classes of Ermakov systems.

Applied algebraic reduction to find symmetries.

Enhanced the symmetry analysis of Ermakov systems.

Abstract

Symmetry analysis of Ermakov systems has attracted enormous treatments in recent times. In this paper we consider three classes of the Ermakov systems and obtain their nonlocal symmetries using a simple algebraic reduction process. We observed that these nonlocal symmetries are new to the literature.