title: Effects of parity-time symmetry in nonlinear Klein-Gordon models and their stationary kinks.
abstract: In this work, we introduce some basic principles of PT-symmetric Klein-Gordon nonlinear field theories. By formulating a particular antisymmetric gain and loss profile, we illustrate that the stationary states of the model do not change. However, the stability critically depends on the gain and loss profile. For a symmetrically placed solitary wave (in either the continuum model or a discrete analog of the nonlinear Klein-Gordon type), there is no effect on the steady state spectrum. However, for asymmetrically placed solutions, there exists a measurable effect of which a perturbative mathematical characterization is offered. It is generally found that asymmetry towards the lossy side leads towards stability, while towards the gain side produces instability. Furthermore, a host of finite size effects, which disappear in the infinite domain limit, are illustrated in connection to the continuous spectrum of the problem.
authors.affiliation: Mathematics Department, University of Hartford, 200 Bloomeld Avenue, West Hartford, Connecticut 06112, USA.
authors.forename: A
authors.initials: A
authors.lastname: Demirkaya
authors.forename: D J
authors.initials: DJ
authors.lastname: Frantzeskakis
authors.forename: P G
authors.initials: PG
authors.lastname: Kevrekidis
authors.forename: A
authors.initials: A
authors.lastname: Saxena
authors.forename: A
authors.initials: A
authors.lastname: Stefanov