Linear and Nonlinear PT-symmetric Oligomers: A Dynamical Systems Analysis

Abstract

In the present work we focus on the cases of two-site (dimer) and three-site (trimer) configurations, i.e. oligomers, respecting the parity-time (PT) symmetry, i.e., with a spatially odd gain-loss profile. We examine different types of solutions of such configurations with linear and nonlinear gain/loss profiles. Solutions beyond the linear PT-symmetry critical point as well as solutions with asymmetric linearization eigenvalues are found in both the nonlinear dimer and trimer. The latter feature is absent in linear PT-symmetric trimers, while both of them are absent in linear PT symmetric dimers. Furthermore, nonlinear gain/loss terms enable the existence of both symmetric and asymmetric solution profiles (and of bifurcations between them), while only symmetric solutions are present in the linear PT-symmetric dimers and trimers. The linear stability analysis around the obtained solutions is discussed and their dynamical evolution is explored by means of direct numerical simulations. Finally, a brief discussion is also given of recent progress in the context of PT-symmetric quadrimers.

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Cited by in corpus (27)

• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Nonlinear switching and solitons in PT-symmetric photonic systems
• Continuous and discrete Schrodinger systems with PT-symmetric nonlinearities
• Integrable nonlocal vector nonlinear Schrödinger equation with self-induced parity-time-symmetric Potential
• Hamiltonian formulation of the standard $\mathcal{P}\mathcal{T}$-symmetric nonlinear Schrödinger dimer
• Dimer with gain and loss: Integrability and $\mathcal{P}\mathcal{T}$-symmetry restoration
• On Symmetries and Exact Solutions of a Class of Non-local Non-linear Schrodinger Equations with Self-induced PT-symmetric Potential
• On the integrability of PT-symmetric dimers
• Peregrine Rogue Wave dynamics in the continuous nonlinear Schrödinger system with parity-time symmetric Kerr nonlinearity
• Revisiting the PT-symmetric Trimer: Bifurcations, Ghost States and Associated Dynamics
• Chiral current circulation and $\mathcal{P}\mathcal{T}$ symmetry in a trimer of oscillators
• Stationary modes and integrals of motion in nonlinear lattices with PT-symmetric linear part
• $\mathcal{P}\mathcal{T}$ symmetric phase transition and single-photon transmission in an optical trimmer system
• Exceptional points in oligomer chains
• Peregrine rogue waves in the nonlocal nonlinear Schrödinger equation with parity-time symmetric self-induced potential
• Parity-time-symmetric closed form optical quadrimer waveguides
• PT-symmetry Management in Oligomer Systems
• Two-dimensional solitons in conservative and parity-time-symmetric triple-core waveguides with cubic-quintic nonlinearity
• Quasi-energies, parametric resonances, and stability limits in ac-driven $\mathcal{P}\mathcal{T}$-symmetric systems
• $\mathcal{P}\mathcal{T}-$Symmetric Dimers with Time-Periodic Gain/Loss Function
• Exceptional point in a coupled Swanson system
• Nonlinear Parity-Time (PT) symmetric closed-form optical quadrimer waveguides: Attractor perspective
• Coherent population oscillations and an effective spin-exchange interaction in a $\mathcal{P}\mathcal{T}$ symmetric polariton mixture
• Highly Amplified Light Transmission in Parity-Time Symmetric Multilayered Structure
• Integrability and trajectory confinement in $\mathcal{P}\mathcal{T}$-symmetric waveguide arrays
• Non-reciprocal population dynamics in a quantum trimer
• Nonlinear modes and symmetries in linearly-coupled pairs of PT-invariant dimers