We study the interplay between nonlinearity and the non-Hermitian skin effect in the nonlinear Su-Schrieffer-Heeger model. Using a fixed-point approach, we derive stability conditions for nonlinear skin modes (skin solitons) and show that linear and nonlinear skin mode spectra coincide for semi-infinite systems. Nonlinearity typically opposes skin localization, leading to antilocalization above a critical amplitude. In finite open-boundary lattices, the model supports continuous families of edge gap solitons arising from linear zero-energy states. They become unstable in the semi-infinite limit, where strong-nonlinearity skin modes emerge. Finally, we demonstrate hysteresis in the bifurcation structure.

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• Bifurcations
• Topological effects in photonic systems
• Non-Hermitian systems
• Solitons