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.