Lie symmetries and infinite-dimensional Lie algebras of certain nonlinear dissipative systems

Abstract

We point out that the dissipative force-free Duffing oscillator and Holmes-Rand nonlinear oscillator admit infinite dimensional symmetry algebras for certain parametric choices for which the systems become integrable. From the nature of the symmetry vector fields one can also write down the integrals of motion for the above systems. In addition we point out that the other dissipative systems discussed in the literature also admit infinite dimensional Lie algebras.