Abstract
We use a small-amplitude multiple scale expansion to investigate the existence of shock waves in a chain of two-level atoms with both exchange and dipole-dipole interactions. We show that the exchange interaction allows the formation of the system of both bright and dark shock waves. Conversely, the dipole-dipole interaction results in the instability of the background and, as a consequence, in the prevention of the formation of shock waves. The analytical results are found to be in good qualitative agreement with a direct numerical integration of the system.
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