Abstract
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.
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