Susanto, H and Kusdiantara, R and Li, N and Kirikchi, OB and Adzkiya, D and Putri, ERM and Asfihani, T (2018) Snakes and ghosts in a parity-time-symmetric chain of dimers. Physical Review E, 97 (6). 062204-. DOI https://doi.org/10.1103/PhysRevE.97.062204
Susanto, H and Kusdiantara, R and Li, N and Kirikchi, OB and Adzkiya, D and Putri, ERM and Asfihani, T (2018) Snakes and ghosts in a parity-time-symmetric chain of dimers. Physical Review E, 97 (6). 062204-. DOI https://doi.org/10.1103/PhysRevE.97.062204
Susanto, H and Kusdiantara, R and Li, N and Kirikchi, OB and Adzkiya, D and Putri, ERM and Asfihani, T (2018) Snakes and ghosts in a parity-time-symmetric chain of dimers. Physical Review E, 97 (6). 062204-. DOI https://doi.org/10.1103/PhysRevE.97.062204
Abstract
We consider linearly coupled discrete nonlinear Schrödinger equations with gain and loss terms and with a cubic-quintic nonlinearity. The system models a parity-time (PT)-symmetric coupler composed by a chain of dimers. We study uniform states and site-centered and bond-centered spatially localized solutions and present that each solution has a symmetric and antisymmetric configuration between the arms. The symmetric solutions can become unstable due to bifurcations of asymmetric ones, that are called ghost states, because they exist only when an otherwise real propagation constant is taken to be complex valued. When a parameter is varied, the resulting bifurcation diagrams for the existence of standing localized solutions have a snaking behavior. The critical gain and loss coefficient above which the PT symmetry is broken corresponds to the condition when bifurcation diagrams of symmetric and antisymmetric states merge. Past the symmetry breaking, the system no longer has time-independent states. Nevertheless, equilibrium solutions can be analytically continued by defining a dual equation that leads to ghost states associated with growth or decay, that are also identified and examined here. We show that ghost localized states also exhibit snaking bifurcation diagrams. We analyze the width of the snaking region and provide asymptotic approximations in the limit of strong and weak coupling where good agreement is obtained.
Item Type: | Article |
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Subjects: | Q Science > QA Mathematics |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 27 Jun 2018 10:49 |
Last Modified: | 07 Aug 2024 18:40 |
URI: | http://repository.essex.ac.uk/id/eprint/22330 |
Available files
Filename: 1805.12478.pdf