  In this paper we introduce models of short wave-long wave interactions in the
relativistic setting. In this context the nonlinear Schr\"odinger equation is
no longer adequate for describing short waves and is replaced by a nonlinear
Dirac equation. Two specific examples are considered: the case where the long
waves are governed by a scalar conservation law; and the case where the long
waves are governed by the augmented Born-Infeld equations in electromagnetism.
