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We present a relativistic generalization of the nonlinear Schrodinger equation, the nonlinear Dirac equation (NLDE).Although different versions of a nonlinear Dirac equation have appeared in numerous fields in the past (for a recent summary, see [1]), we present a novel version of the NLDE which is of immediate experimental relevance in Bose-Einstein condensates and has a "speed of light" ten orders of magnitude slower than c.We discuss the symmetry properties of this new equation.