Solitons mediated by skin-mode localization and band nonreciprocity.

Solitons typically arise from the competition between band dispersion and nonlinearity. In lattices exhibiting the non-Hermitian skin effect, increasing nonlinearity induces a transition in localization from linear skin modes to solitons. However, localization alone does not clarify how skin modes and band dispersion contribute to soliton formation or classification. Here, by formulating a Wannier-projected effective nonlinear Hamiltonian, we show that soliton formation is determined by how skin-mode localization and band nonreciprocity suppress or enhance wave dispersion, giving rise to two distinct families: skin-mode-assisted solitons (SMASs) and nonreciprocity-dressed solitons (NRDSs). Using a stacked Su-Schrieffer-Heeger-like model as a prototype, we construct the soliton threshold diagram and analytically demonstrate that increasing nonreciprocity lowers the SMAS threshold but raises that of NRDSs. We further extend the framework to higher dimensions and more complex lattices, establishing its generality. This work provides predictive tools for understanding and engineering solitons in experimentally realizable non-Hermitian systems.