Dynamics of a Completely Integrable $N$-Coupled Liénard Type Nonlinear Oscillator

Details Dynamics of a Completely Integrable $N$-Coupled Liénard Type Nonlinear Oscillator Dynamics of a Completely Integrable $N$-Coupled Liénard Type Nonlinear Oscillator

2008-10-10

arxiv.org/abs/0810.1821v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

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Scientific paper

We present a system of $N$-coupled Li\'enard type nonlinear oscillators which is completely integrable and possesses explicit $N$ time-independent and $N$ time-dependent 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 quasiperiodic 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.

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