  Non-linear effects and non-Hermitian phenomena unveil additional intricate
facets in topological matter physics. They can naturally intertwine to enable
advanced functionalities in topoelectrical circuits and photonic structures.
Here, we illustrate the subtle interplay between nonlinearity and
non-Hermiticity by examining the characteristics of small wave perturbations on
the background of the self-induced topological edge state in the nonlinear
Su-Schrieffer-Heeger model. We demonstrate that their underlying physics is
captured by the non-Hermitian effective Hamiltonian, which features
nonreciprocal coupling terms and entails unconventional time-dependent field
localization.
