Snakes and ghosts in a parity-time-symmetric chain of dimers
Phys. Rev. E 97, 062204 (2018) We consider linearly coupled discrete nonlinear Schr\"odinger equations with gain and loss terms and with a cubic-quintic nonlinearity. The system models a parity-time ($\cal{PT}$)-symmetric coupler composed by a chain of dimers. Particularly we study site-centere...
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| Main Authors: | , , , , , , |
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| Format: | Journal Article |
| Language: | English |
| Published: |
31-05-2018
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| Subjects: | |
| Online Access: | Get full text |
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| Summary: | Phys. Rev. E 97, 062204 (2018) We consider linearly coupled discrete nonlinear Schr\"odinger equations with
gain and loss terms and with a cubic-quintic nonlinearity. The system models a
parity-time ($\cal{PT}$)-symmetric coupler composed by a chain of dimers.
Particularly we study site-centered and bond-centered spatially-localized
solutions and present that each solution has a symmetric and antisymmetric
configuration between the arms. When a parameter is varied, the resulting
bifurcation diagrams for the existence of standing localized solutions have a
snaking behaviour. The critical gain/loss coefficient above which the
$\cal{PT}-$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 so-called 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 analyse the width of the snaking
region and provide asymptotic approximations in the limit of strong and weak
coupling where good agreement is obtained. |
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| DOI: | 10.48550/arxiv.1805.12478 |