Traveling chimera states

In this paper we consider the Ott-Antonsen equation describing the long time coarse-grained dynamics of a ring of nonlocally coupled phase oscillators. We study traveling wave solutions relevant to traveling chimera states in the coupled oscillator system. In particular, we derive and rigorously justify asymptotic formulas for traveling wave solutions in the case of small asymmetry of nonlocal coupling. We also show that the Ott-Antonsen equation provides a reliable description of traveling chimera states for heterogeneous oscillators (with Lorentzian distribution of natural frequencies), but fails to do this for identical oscillators.