Discrete nonlocal nonlinear Schrodinger equation on graphs: Dynamics of PT-symmetric solitons in discrete networks

We consider discrete nonlocal nonlinear Schrodinger equation proposed earlier by Ablowitz and Musslimani, on a branched 1D lattice, presented in terms of the graphs with discrete bonds. The soliton solutions are derived for some simplest (star and tree) graphs. Numerical solutions are obtained for the cases, when the problem does not approve the analytical one. Integrability of the problem is shown by proving existence of infinite number of conservation laws.(c) 2022 Elsevier B.V. All rights reserved.