Coupled nonlinear schrödinger equations with gain and loss: Modeling PT symmetry

Abstract

Coupled nonlinear Schrödinger (NLS) equations is an ubiquitous model describing wave propagation in diverse physical systems. In combination with gain and loss exactly balanced with each other, this model allows for modeling parity (P) and time (T) symmetries in frameworks beyond the non-Hermitian quantum mechanics, where they have been introduced originally. Being open, i.e. not conserving energy, such systems nevertheless bear many properties which are characteristic for conservative models. This allows one to explore various wave phenomena in PT -symmetric settings, including bright and dark solitons and their interactions with defects, soliton switches, resonant wave interactions, wave collapse, etc. In this Chapter an overview of some recent results on these processes is presented. The outcomes are interpreted in contexts of nonlinear optics and matter wave theory.