ABSTRACT
Parity-Time (PT)- symmetric systems have become a topic which has generated considerable research interest. This chapter discusses nonlinear wave propagation in the presence of linear potentials possessing PT symmetry. It considers in particular the localized case, consisting of a bell-shaped trapping potential, and periodic potentials, infinitely extended across the transverse plane. The chapter explains the linear spectrum of the structures. It shows which types of solitons are supported by the system, comprising their stability. The chapter explores that PT systems predominantly exhibit oscillatory instability, with the eigenvalues of the perturbation modes appearing in quartets, the latter being in the complex plane of the vertices of a square centered in the origin. Bright solitons in periodic potentials show a vast phenomenology, much more heterogeneous than in homogeneous systems or in single-humped potentials. The chapter discusses qualitatively what is going on in a focusing nonlinear material with a periodic potential written on it.
