Nonlinear stationary states in PT-symmetric lattices
Abstract
In the present work we examine both the linear and nonlinear properties of two related 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 at an analogue of the anti-continuum limit for the dNLS equation. Secondly, we consider the case when a finite PT-dNLS chain is embedded as a defect in the infinite dNLS lattice. We show that the stability intervals of the infinite PT-dNLS lattice are wider than in the case of a finite PT-dNLS chain. We also prove existence of localized stationary states (discrete solitons) in the analogue of the anti-continuum limit for the dNLS equation. Numerical computations illustrate the existence of nonlinear stationary states, as well as the stability and saddle-center bifurcations of discrete solitons.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2013
- DOI:
- 10.48550/arXiv.1303.3298
- arXiv:
- arXiv:1303.3298
- Bibcode:
- 2013arXiv1303.3298K
- Keywords:
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- Nonlinear Sciences - Pattern Formation and Solitons;
- Mathematics - Dynamical Systems
- E-Print:
- 28 pages