On the symmetries of a nonlinear non-polynomial oscillator

TL;DR

This paper explores various symmetries of a nonlinear non-polynomial oscillator, including adjoint-symmetries, contact symmetries, and telescopic vector fields, and derives related mathematical quantities using a theorem.

Contribution

It introduces a procedure to identify multiple symmetry types and related quantities for a class of nonlinear oscillators based on a theorem by Muriel and Romero.

Findings

Identification of adjoint-symmetries, contact symmetries, and telescopic vector fields.

Derivation of Jacobi last multipliers and Darboux polynomials.

Procedure applicable to a broad class of nonlinear oscillator equations.

Abstract

In this paper, we unearth symmetries of different types of a nonlinear non-polynomial oscillator. The symmetries which we report here are adjoint-symmetries, contact symmetries and telescopic vector fields. We also obtain Jacobi last multipliers and Darboux polynomials as a by-product of our procedure. All the aforementioned quantities are derived from a Theorem proved by Muriel and Romero. The procedure which we present here is applicable to a class of nonlinear oscillator equations.