  We study solitons of the two-dimensional nonlinear Dirac equation with
asymmetric cubic nonlinearity. We show that, with the nonlinearity parameters
specifically tuned, a high degree of localization of both spinor components is
enabled on a ring of certain radius. Such ring Dirac soliton can be viewed as a
self-induced nonlinear domain wall and can be implemented in nonlinear photonic
graphene lattice with Kerr-like nonlinearities. Our model could be instructive
for understanding localization mechanisms in nonlinear topological systems.
