On the integrability of PT-symmetric dimers

Abstract

The coupled discrete linear and Kerr nonlinear Schrodinger equations with gain and loss describing transport on dimers with parity-time PT symmetric potentials are considered. The model is relevant among others to experiments in optical couplers and proposals on Bose-Einstein condensates in PT symmetric double-well potentials. It is known that the models are integrable. Here, the integrability is exploited further to construct the phase-portraits of the system. A pendulum equation with a linear potential and a constant force for the phase-difference between the fields is obtained, which explains the presence of unbounded solutions above a critical threshold parameter. The behaviour of all solutions of the system, including changes in the topological structure of the phase-plane, is then discussed.

To appear in Physical Review A

References in corpus (9)

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Cited by in corpus (25)

• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Nonlinear switching and solitons in PT-symmetric photonic systems
• Discrete solitons and vortices on two-dimensional lattices of $\mathcal{P}\mathcal{T}$-symmetric couplers
• Hamiltonian formulation of the standard $\mathcal{P}\mathcal{T}$-symmetric nonlinear Schrödinger dimer
• Nonlinear dynamics in PT-symmetric lattices
• Dimer with gain and loss: Integrability and $\mathcal{P}\mathcal{T}$-symmetry restoration
• Jamming anomaly in $\mathcal{P}\mathcal{T}$-symmetric systems
• Nonlinear modes in a generalized $\mathcal{P}\mathcal{T}$-symmetric discrete nonlinear Schrödinger equation
• Discrete solitons and scattering of lattice waves in guiding arrays with a nonlinear $\mathcal{P}\mathcal{T}$-symmetric defect
• Solitons in PT-symmetric ladders of optical waveguides
• Interaction of sine-Gordon kinks and breathers with a $\mathcal{P}\mathcal{T}$-symmetric defect
• Discrete solitons in self-defocusing systems with $\mathcal{P}\mathcal{T}$-symmetric defects
• Snakes and ghosts in a parity-time-symmetric chain of dimers
• Quasi-energies, parametric resonances, and stability limits in ac-driven $\mathcal{P}\mathcal{T}$-symmetric systems
• Global existence of solutions to coupled $\mathcal{P}\mathcal{T}$-symmetric nonlinear Schrödinger equations
• Generalized Dimers and their Stokes-variable Dynamics
• $\mathcal{P}\mathcal{T}-$Symmetric Dimers with Time-Periodic Gain/Loss Function
• Non-Hermitian dynamics of a two-spin system with PT symmetry
• Systems that become $\mathcal{P}\mathcal{T}$ symmetric through interaction
• Integrability and trajectory confinement in $\mathcal{P}\mathcal{T}$-symmetric waveguide arrays
• Energy-recurrence Breakdown and Chaos in Disordered Fermi-Pasta-Ulam-Tsingou Lattices
• PT-symmetry in quasi-integrable models
• Breathers in Hamiltonian $\mathcal{P}\mathcal{T}$-symmetric chains of coupled pendula under a resonant periodic force
• Solitonic dynamics and excitations of the nonlinear Schrodinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials
• Discrete solitons dynamics in $\mathcal{P}\mathcal{T}$-symmetric oligomers with complex-valued couplings