We prove the existence of nonlinear normal modes for general systems of two coupled nonlinear oscillators. Facilitating the comparison principle for ordinary differential equations it is shown that there exist exact solutions representing a vibration in unison of the system. The associated spatially localised time-periodic solutions feature out-of-phase and in-phase motion of the oscillators.
@article{arxiv.1406.4755,
title = {Existence of nonlinear normal modes for coupled nonlinear oscillators},
author = {Dirk Hennig},
journal= {arXiv preprint arXiv:1406.4755},
year = {2015}
}