Dynamics of a completely integrable N-coupled Lienard-type nonlinear oscillator

Abstract

We present a system of N-coupled Lienard-type nonlinear oscillators which is completely integrable and possesses N time-independent and N time-dependent explicit integrals. In a special case, it becomes maximally superintegrable and admits (2N - 1) time-independent integrals. The results are illustrated for the N = 2 and arbitrary number cases. General explicit periodic (with frequency independent of amplitude) and quasi-periodic solutions as well as decaying-type/frontlike solutions are presented, depending on the signs and magnitudes of the system parameters. Though the system is of a nonlinear damped type, our investigations show that it possesses a Hamiltonian structure and that under a contact transformation it is transformable to a system of uncoupled harmonic oscillators.