Travelling Wave in the Generalized Kuramoto Model with Inertia

We study the dynamics of the generalized Kuramoto model with inertia, in which oscillators with positive coupling strength are conformists and oscillators with negative coupling strength are contrarians. By numerically simulating the model, we find that the model supports a modulated travelling wave state except for already displayed travelling wave states and \pi state in previous literature. The modulated travelling wave state may be characterized by the phase distributions of oscillators. Finally, the modulated travelling wave state and the travelling wave state of the model in the parameter space are presented.