On the Lie symmetries of a class of generalized Ermakov systems

TL;DR

This paper extends the symmetry analysis of Ermakov systems to a generalized class where frequency depends on dynamical variables, enabling exact solutions for a broader set of nonlinear coupled oscillators.

Contribution

It introduces a generalized framework for Ermakov systems with variable-dependent frequency and provides exact solutions for these complex systems.

Findings

Extended symmetry analysis for variable-dependent frequency

Exact closed-form solutions for generalized Ermakov systems

Hamiltonian formulation of nonlinear coupled oscillators

Abstract

The symmetry analysis of Ermakov systems is extended to the generalized case where the frequency depends on the dynamical variables besides time. In this extended framework, a whole class of nonlinearly coupled oscillators are viewed as Hamiltonian Ermakov system and exactly solved in closed form.