Discrete extreme waves from a single non-hermitian coupling defect

Abstract In discrete nonlinear systems, rogue waves typically emerge when the system has initial excitations. We consider a nonlinear Hermitian tight-binding lattice with a single localized impurity, modeled by a discrete nonlinear Schrödinger equation. In this study, we assume that the background is initially uniform, and show that a single impurity in the system can lead to the formation of an extreme waves. Our findings suggest that impurity-driven rogue waves can arise without any initial excitation profile, which may have implications for photonic lattices and other engineered nonlinear systems.