  We analyse a nonlinear QW model which can be experimentally implemented using
the components of the electric field on an optical nonlinear Kerr medium, which
translates into a rotation in the coin operator, with an angle which depends
(in a nonlinear fashion) on the state of the walker. This simple dependence
makes it easy to consider the space-time continuum limit of the evolution
equation, which takes the form of a nonlinear Dirac equation. The analysis of
this continuum limit allows us, under some approximations, to gain some insight
into the nature of soliton structures, which is illustrated by our numerical
calculations. These solitons are stable structures whose trajectories can be
modulated by choosing the appropriate initial conditions. We have also studied
the stability of solitons when they are subject to an additional phase that
simulates an external electric field, and also explored if they are formed in
higher dimensional spaces.
