# Nonlinear Stationary States in PT-Symmetric Lattices

@article{Kevrekidis2013NonlinearSS, title={Nonlinear Stationary States in PT-Symmetric Lattices}, author={Panayotis G. Kevrekidis and Dmitry E. Pelinovsky and Dmitry Tyugin}, journal={SIAM J. Appl. Dyn. Syst.}, year={2013}, volume={12}, pages={1210-1236} }

In the present work we examine both the linear and nonlinear properties of two related parity-time (PT)-symmetric systems of the discrete nonlinear Schrodinger (dNLS) type. First, we examine the parameter range for which the finite PT-dNLS chains have real eigenvalues and PT-symmetric linear eigenstates. We develop a systematic way of analyzing the nonlinear stationary states with the implicit function theorem. Second, we consider the case when a finite PT-dNLS chain is embedded as a defect in…

## 38 Citations

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We consider finite-dimensional nonlinear systems with linear part described by a parity-time (PT-) symmetric operator. We investigate bifurcations of stationary nonlinear modes from the eigenstates…

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Discrete solitons and vortices on two-dimensional lattices of PT-symmetric couplers.

- PhysicsOptics express
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This work introduces a 2D network built of PT-symmetric dimers with on-site cubic nonlinearity, the gain and loss elements of the dimers being linked by parallel square-shaped lattices, and finds that unstable OnVs do not blow up, but spontaneously rebuild themselves into stable FSs.

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We explain the concept of Krein signature in Hamiltonian and PT symmetric systems on the case study of the one-dimensional Gross–Pitaevskii equation with a real harmonic potential and an imaginary…

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