Dynamics of a generalized PT-symmetric discrete nonlinear Schroedinger equation

Dmitry A. Zezyulin, Dmitry E. Pelinovsky, Vladimir V. Konotop

University of Lisbon, Portugal

We consider a generalized network of the discrete nonlinear Schroedinger type. The network consists of $2N$ sites (waveguides) where $N$ is finite. The model is PT symmetric, i.e. it contains terms with gain and dissipation which compensate each other. The network accounts for the Kerr-type nonlinearity as well as for inter-site nonlinear coupling. We pay the main attention to the the dimer model ($N=1$). We show that even in the case of the unbroken PT symmetry this model has solutions unbounded in time. We also discover a new integrable configuration of the PT-symmetric dimer. All solutions of the integrable model are bounded in time provided that PT symmetry is unbroken. We will also touch upon dynamics of a stochastic PT-symmetric dimer. For arbitrary finite $N$, we present sufficient conditions of the unbroken and broken PT symmetry of the linear problem and discuss the existence and stability of stationary nonlinear modes.