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 ultracold quantum gases and has a "speed of light" ten orders of magnitude slower than c. We discuss the symmetry properties of this new equation, among which are that it breaks the principle of relativity (Poincare covariance) and it maintains CPT symmetry (charge conjugation x parity x time reversal).
[1] Wei-Khim Ng and Rajesh R. Parwani, e-print arXiv:0707.1553 (2007).