Time Periodic Extreme Waves in a Non-Hermitian Lattice

Abstract

Periodic extreme waves, characterized by their recurrent and exceptionally high amplitudes, have gained significant attention in various scientific disciplines. In this study, we consider a nonreciprocal DNLS equation with position-dependent nonlinear interaction strength. We show that time-periodic extreme waves can occur in a non-Hermitian lattice. We also demonstrate that long-living discrete extreme waves is possible when considering proper position-dependent nonlinear interaction strength in a non-Hermitian system.