  Graphene's honeycomb lattice structure is quite remarkable in the sense that
it leads, in the long wavelength limit, to a massless Dirac equation
description of nonrelativistic quasiparticles associated with electrons and
holes present in the two dimensional crystallite. In the case of cold bosonic
atoms trapped in a honeycomb optical lattice, Haddad and Carr (2009) have
recently shown, by taking into account binary contact interactions, that the
dynamics of these Bose-Einstein condensates is governed by a nonlinear Dirac
equation (NLDE). In this paper, we study exact stationary solutions of such a
NLDE. After proving that the energy eigenvalues are real, we show that the sum
of orbital angular momentum and pseudospin angular momentum normal to the
crystal commutes with the nonlinear Hamiltonian whenever magnitudes of the
pseudospin components do not depend on the polar angle $\phi $. We obtain some
exact stationary and localized solutions of the NLDE.
