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We analyse a nonlinear QW model which can be experimentally implemented usingthe components of the electric field on an optical nonlinear Kerr medium, whichtranslates into a rotation in the coin operator, with an angle which depends(in a nonlinear fashion) on the state of the walker. This simple dependencemakes it easy to consider the space-time continuum limit of the evolutionequation, which takes the form of a nonlinear Dirac equation. The analysis ofthis continuum limit allows us, under some approximations, to gain some insightinto the nature of soliton structures, which is illustrated by our numericalcalculations. These solitons are stable structures whose trajectories can bemodulated by choosing the appropriate initial conditions. We have also studiedthe stability of solitons when they are subject to an additional phase thatsimulates an external electric field, and also explored if they are formed inhigher dimensional spaces.

Solitons in a photonic nonlinear quantum walk: lessons from the continuum