  We study analytically and numerically an optical analogue of Dirac solitons
in binary waveguide arrays in presence of Kerr nonlinearity.
Pseudo-relativistic soliton solutions of the coupled-mode equations describing
dynamics in the array are analytically derived. We demonstrate that with the
found soliton solutions, the coupled mode equations can be converted into the
nonlinear relativistic 1D Dirac equation. This paves the way for using binary
waveguide arrays as a classical simulator of quantum nonlinear effects arising
from the Dirac equation, something that is thought to be impossible to achieve
in conventional (i.e. linear) quantum field theory.
