We study waves in a chain of dispersively coupled phase oscillators. Two approaches--a quasicontinuous approximation and an iterative numerical solution of the lattice equation--allow us to characterize different types of traveling waves: compactons, kovatons, solitary waves with exponential tails as well as a novel type of semicompact waves that are compact from one side. Stability of these waves is studied using numerical simulations of the initial value problem.
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