title: Interaction of sine-Gordon kinks and breathers with a parity-time-symmetric defect.
abstract: The scattering of kinks and low-frequency breathers of the nonlinear sine-Gordon (SG) equation on a spatially localized parity-time-symmetric perturbation (defect) with a balanced gain and loss is investigated numerically. It is demonstrated that if a kink passes the defect, it always restores its initial momentum and energy, and the only effect of the interaction with the defect is a phase shift of the kink. A kink approaching the defect from the gain side always passes, while in the opposite case it must have sufficiently large initial momentum to pass through the defect instead of being trapped in the loss region. The kink phase shift and critical velocity are calculated by means of the collective variable method. Kink-kink (kink-antikink) collisions at the defect are also briefly considered, showing how their pairwise repulsive (respectively, attractive) interaction can modify the collisional outcome of a single kink within the pair with the defect. For the breather, the result of its interaction with the defect depends strongly on the breather parameters (velocity, frequency, and initial phase) and on the defect parameters. The breather can gain some energy from the defect and as a result potentially even split into a kink-antikink pair, or it can lose a part of its energy. Interestingly, the breather translational mode is very weakly affected by the dissipative perturbation, so that a breather penetrates more easily through the defect when it comes from the lossy side, than a kink. In all studied soliton-defect interactions, the energy loss to radiation of small-amplitude extended waves is negligible.
authors.affiliation: Department of Physics, Ferdowsi University of Mashhad, 91775-1436 Mashhad, Iran.
authors.forename: Danial
authors.initials: D
authors.lastname: Saadatmand
authors.affiliation: Institute for Metals Superplasticity Problems RAS, Khalturin 39, 450001 Ufa, Russia and Saint Petersburg State Polytechnical University, Politekhnicheskaya 29, 195251 St. Petersburg, Russia.
authors.forename: Sergey V
authors.initials: SV
authors.lastname: Dmitriev
authors.affiliation: Institute of Mathematics CC USC RAS, Chernyshevsky 112, 450008 Ufa, Russia and Bashkir State Pedagogical University, October Rev. 3a, 450000 Ufa, Russia.
authors.forename: Denis I
authors.initials: DI
authors.lastname: Borisov
authors.affiliation: Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003, USA.
authors.forename: Panayotis G
authors.initials: PG
authors.lastname: Kevrekidis