Generation of strongly localized skin solitons in non-Hermitian waveguide arrays with the Kerr effect

Abstract: We address two distinct nonlinear propagation problems in nonlinear optical waveguide arrays (WGAs) with non-reciprocal (non-Hermitian) couplings. First, we investigate the light propagation launched by initial excitations of two different types. The single-channel excitation creates stable solitons supported by the interplay of the Kerr nonlinearity and non-Hermitian skin effect (NHSE). In this case, we derive, by means of the symbolic-regression method, an analytical formula defining the soliton existence boundary. For the broad-pulse excitation, we produce perturbed soliton solutions analytically in the continuum approximation, which is accurately corroborated by numerical results. We thus conclude that NHSE accelerates the propagation of the broad soliton towards the boundary, ultimately causing tight localization at the edge, which is a hallmark of the NHSE in the continuum limit. Second, we identify stationary solitons in the system -- specifically, nonlinear bulk modes in the Hermitian regime and near-edge skin solitons in the non-Hermitian one. The nonlinear bulk modes are compressed toward the edge of the WGA under the action of the non-reciprocality, which is the nonlinear extension of NHSE.