A class of solvable coupled nonlinear oscillators with amplitude independent frequencies

Existence of amplitude independent frequencies of oscillation is an unusual property for a nonlinear oscillator. We find that a class of N coupled nonlinear Liénard type oscillators exhibit this interesting property. We show that a specific subset can be explicitly solved from which we demonstrate the existence of periodic and quasiperiodic solutions. Another set of N coupled nonlinear oscillators, possessing the amplitude independent nature of frequencies, is almost integrable in the sense that the system can be reduced to a single nonautonomous first order scalar differential equation which can be easily integrated numerically.

► We obtain a class of coupled nonlinear oscillators admitting oscillatory type solutions whose frequencies of oscillations are independent of the amplitudes. ► The system is found to admit periodic and quasiperiodic behavior for suitable parametric choices. ► This system of N coupled nonlinear oscillators is reduced to a single first order ordinary differential equation. ► Complete integrability is proved for a specific parametric choice by obtaining the general solution. ► Another set of N coupled oscillators is proved to be almost integrable.