Nonlinear modes in a generalized $\mathcal{P}\mathcal{T}$-symmetric discrete nonlinear Schrödinger equation

Abstract

We generalize a finite parity-time ($\mathcal{P}\mathcal{T}$-) symmetric network of the discrete nonlinear Schrödinger type and obtain general results on linear stability of the zero equilibrium, on the nonlinear dynamics of the dimer model, as well as on the existence and stability of large-amplitude stationary nonlinear modes. A result of particular importance and novelty is the classification of all possible stationary modes in the limit of large amplitudes. We also discover a new integrable configuration of a $\mathcal{P}\mathcal{T}$-symmetric dimer.

20 pages, 1 figure; accepted to J. Phys. A: Math. Theor

References in corpus (8)

• Unidirectional Nonlinear PT-symmetric Optical Structures
• Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
• $\mathcal{P}\mathcal{T}$-symmetry breaking in a necklace of coupled optical waveguides
• Discrete solitons in PT-symmetric lattices
• Nonlinear dynamics in PT-symmetric lattices
• On the integrability of PT-symmetric dimers
• Internal modes of discrete solitons near the anti-continuum limit of the dNLS equation
• Stationary modes and integrals of motion in nonlinear lattices with PT-symmetric linear part

Cited by in corpus (15)

• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Nonlinear switching and solitons in PT-symmetric photonic systems
• Dimer with gain and loss: Integrability and $\mathcal{P}\mathcal{T}$-symmetry restoration
• Solitons in PT-symmetric ladders of optical waveguides
• Interaction of sine-Gordon kinks and breathers with a $\mathcal{P}\mathcal{T}$-symmetric defect
• Topological edge-states of the PT-symmetric Su-Schrieffer-Heeger model: An effective two-state description
• Spinor solitons and their $\mathcal{P}\mathcal{T}$-symmetric offspring
• Stabilization of the coupled pendula chain under parametric PT-symmetric driving force
• Two-dimensional solitons in conservative and parity-time-symmetric triple-core waveguides with cubic-quintic nonlinearity
• Functional control of network dynamics using designed Laplacian spectra
• Generalized Dimers and their Stokes-variable Dynamics
• Global existence of solutions to coupled $\mathcal{P}\mathcal{T}$-symmetric nonlinear Schrödinger equations
• Long-time stability of breathers in Hamiltonian $\mathcal{P}\mathcal{T}$-symmetric lattices
• Systems that become $\mathcal{P}\mathcal{T}$ symmetric through interaction
• Existence and stability of PT-symmetric vortices in nonlinear two-dimensional square lattices