# 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…

## 36 Citations

Existence and stability of PT-symmetric states in nonlinear two-dimensional square lattices

- Mathematics, Physics
- 2016

Abstract Solitons and vortices symmetric with respect to simultaneous parity ( P ) and time reversing ( T ) transformations are considered on the square lattice in the framework of the discrete…

Stationary modes and integrals of motion in nonlinear lattices with PT-symmetric linear part

- Mathematics, Physics
- 2013

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…

Nonlinear dynamics in PT-symmetric lattices

- Mathematics, Physics
- 2013

We consider nonlinear dynamics in a finite parity-time-symmetric chain of the discrete nonlinear Schrodinger (dNLS) type. For arbitrary values of the gain and loss parameter, we prove that the…

Bifurcation of nonlinear bound states in the periodic Gross-Pitaevskii equation with 𝒫𝒯-symmetry

- Physics, MathematicsProceedings of the Royal Society of Edinburgh: Section A Mathematics
- 2020

Abstract The stationary Gross–Pitaevskii equation in one dimension is considered with a complex periodic potential satisfying the conditions of the 𝒫𝒯 (parity-time reversal) symmetry. Under rather…

Stability of soliton families in nonlinear Schrödinger equations with non-parity-time-symmetric complex potentials

- Physics
- 2016

Abstract Stability of soliton families in one-dimensional nonlinear Schrodinger equations with non-parity-time ( PT )-symmetric complex potentials is investigated numerically. It is shown that these…

Exponential asymptotics for solitons in PT-symmetric periodic potentials

- Physics, Mathematics
- 2014

Solitons in one-dimensional parity-time (PT)-symmetric periodic potentials are studied using exponential asymptotics. The new feature of this exponential asymptotics is that, unlike conservative…

Nonlinear modes and integrals of motion in finite PT-symmetric systems

- Mathematics
- 2013

We investigate bifurcations of nonlinear modes in parity-time (PT-) symmetric discrete systems. We consider a general class of nonlinearities allowing for existence of the nonlinear modes and address…

Nonlinear modes in a generalized -symmetric discrete nonlinear Schrödinger equation

- Mathematics, Physics
- 2014

We generalize a finite parity-time (PT)-symmetric network of the discrete nonlinear Schr¨ odinger type and obtain general results on linear stability of the zero equilibrium, on the nonlinear…

Nonlinear wave dynamics near phase transition in PT-symmetric localized potentials

- Mathematics, Physics
- 2016

Abstract Nonlinear wave propagation in parity-time symmetric localized potentials is investigated analytically near a phase-transition point where a pair of real eigenvalues of the potential coalesce…

Bifurcation of soliton families from linear modes in non-PT-symmetric complex potentials

- Mathematics, Physics
- 2015

Continuous families of solitons in generalized nonlinear Sch\"odinger equations with non-PT-symmetric complex potentials are studied analytically. Under a weak assumption, it is shown that stationary…

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