# Dynamics of Coupled Oscillator Systems - Abstract

**Omel'chenko, Oleh**

*Traveling chimera states*

In this talk we will describe recent work on traveling chimera states in a one-dimensional ring of nonlocally coupled phase oscillators. In the continuum limit such chimera states appear as traveling wave solutions of the corresponding Ott-Antonsen equation. We will derive asymptotic formulas for slowly moving chimera states and show how to perform numerical continuation of such solutions and analyze their stability. Finally, we will outline some unsolved mathematical problems concerned with the analysis of non-stationary chimera states.