Transparent PT-symmetric nonlinear networks

We study reflectionless wave propagation in networks modeled by the nonlocal nonlinear Schrödinger equation on metric graphs, with transparent boundary conditions applied at the vertices. Using a ‘potential approach’ previously developed for the nonlinear Schrödinger equation, we derive transparent boundary conditions specific to the nonlocal nonlinear Schrödinger equation on metric graphs. These conditions prevent backscattering at the vertices, which is essential for reducing losses in signal, heat, and charge transfer in applications including optical fibers, optoelectronic networks, and low-dimensional materials.