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We study waves in a chain of dispersively coupled phase oscillators. Twoapproaches -- a quasi-continuous approximation and an iterative numericalsolution of the lattice equation -- allow us to characterize different types oftraveling waves: compactons, kovatons, solitary waves with exponential tails aswell as a novel type of semi-compact waves that are compact from one side.Stability of these waves is studied using numerical simulations of the initialvalue problem.

Traveling waves and Compactons in Phase Oscillator Lattices