Nonlinear PT-symmetric plaquettes

Abstract

We introduce four basic two-dimensional (2D) plaquette configurations with onsite cubic nonlinearities, which may be used as building blocks for 2D PT -symmetric lattices. For each configuration, we develop a dynamical model and examine its PT symmetry. The corresponding nonlinear modes are analyzed starting from the Hamiltonian limit, with zero value of the gain-loss coefficient. Once the relevant waveforms have been identified (chiefly, in an analytical form), their stability is examined by means of linearization in the vicinity of stationary points. This reveals diverse and, occasionally, fairly complex bifurcations. The evolution of unstable modes is explored by means of direct simulations. In particular, stable localized modes are found in these systems, although the majority of identified solutions is unstable.

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Cited by in corpus (33)

• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Nonlinear switching and solitons in PT-symmetric photonic systems
• $\mathcal{P}\mathcal{T}$-symmetry breaking in a necklace of coupled optical waveguides
• Stability boundaries and collisions of two-dimensional solitons in PT-symmetric couplers with the cubic-quintic nonlinearity
• Odd-time reversal $PT$ symmetry induced by anti-$PT$-symmetric medium
• Discrete solitons and vortices on two-dimensional lattices of $\mathcal{P}\mathcal{T}$-symmetric couplers
• Linear and Nonlinear PT-symmetric Oligomers: A Dynamical Systems Analysis
• A solvable model for solitons pinned to a PT-symmetric dipole
• Nonlinear dynamics in PT-symmetric lattices
• PT-Symmetric Dimer of Coupled Nonlinear Oscillators
• Revisiting the PT-symmetric Trimer: Bifurcations, Ghost States and Associated Dynamics
• Nonlinear localized modes in PT-symmetric optical media with competing gain and loss
• Revisiting the optical $PT$-symmetric dimer
• Numerical calculation of the complex berry phase in non-Hermitian systems
• Parity-time symmetric optical coupler with birefringent arms
• Analytical stable Gaussian soliton supported by a parity-time-symmetric potential with power-law nonlinearity
• Interaction of sine-Gordon kinks and breathers with a $\mathcal{P}\mathcal{T}$-symmetric defect
• Towards nanoscale multiplexing with parity-time symmetric plasmonic coaxial waveguides
• $\mathcal{P}\mathcal{T}$-symmetric coupler with ${\chi }^{(2)}$ nonlinearity
• Staggered $\mathcal{P}\mathcal{T}$-symmetric ladders with cubic nonlinearity
• Parity-time-symmetric closed form optical quadrimer waveguides
• Exact control of parity-time symmetry in periodically modulated nonlinear optical couplers
• Quasi-energies, parametric resonances, and stability limits in ac-driven $\mathcal{P}\mathcal{T}$-symmetric systems
• The emergence and analysis of Kuramoto-Sakaguchi-like models as an effective description for the dynamics of coupled Wien-bridge oscillators
• PT-symmetric sine-Gordon breathers
• Nonlinear Parity-Time (PT) symmetric closed-form optical quadrimer waveguides: Attractor perspective
• Necklaces of $\mathcal{P}\mathcal{T}$-symmetric dimers
• Mean-field approximation for a Bose-Hubbard dimer with complex interaction strength
• Raising the $\mathcal{P}\mathcal{T}$ transition threshold by strong coupling to neutral chains
• Nonlinear modes and symmetries in linearly-coupled pairs of PT-invariant dimers
• Existence and stability of PT-symmetric vortices in nonlinear two-dimensional square lattices
• Nonlinear stationary states in PT-symmetric lattices
• Characterizing Liouvillian Exceptional Points Through Newton Polygons and Tropical Geometry