Nonlinear stationary states in PTsymmetric lattices
Abstract
In the present work we examine both the linear and nonlinear properties of two related PTsymmetric systems of the discrete nonlinear Schrodinger (dNLS) type. First, we examine the parameter range for which the finite PTdNLS chains have real eigenvalues and PTsymmetric linear eigenstates. We develop a systematic way of analyzing the nonlinear stationary states with the implicit function theorem at an analogue of the anticontinuum limit for the dNLS equation. Secondly, we consider the case when a finite PTdNLS chain is embedded as a defect in the infinite dNLS lattice. We show that the stability intervals of the infinite PTdNLS lattice are wider than in the case of a finite PTdNLS chain. We also prove existence of localized stationary states (discrete solitons) in the analogue of the anticontinuum limit for the dNLS equation. Numerical computations illustrate the existence of nonlinear stationary states, as well as the stability and saddlecenter bifurcations of discrete solitons.
 Publication:

arXiv eprints
 Pub Date:
 March 2013
 arXiv:
 arXiv:1303.3298
 Bibcode:
 2013arXiv1303.3298K
 Keywords:

 Nonlinear Sciences  Pattern Formation and Solitons;
 Mathematics  Dynamical Systems
 EPrint:
 28 pages