Nonlinear skin modes in a non-Hermitian Ablowitz–Ladik-type lattice

The non-Hermitian skin effect (NHSE) has been mostly studied in linear lattices. In nonlinear settings, most studies focus on non-integrable models, while nonlinear lattices with an integrable structure remain less explored. In this study, we examine stationary boundary-localized states in a non-Hermitian nonlinear Ablowitz–Ladik (AL) lattice under open boundary conditions. We show numerically that boundary localization also persists in a nonlinear AL-type lattice, which is integrable in the Hermitian limit. These findings suggest that such an AL-type lattice provides a simple framework for NHSE-type boundary localization.