Dark solitons for a (3+1)-dimensional nonlinear Schrodinger equation with distributed coefficients in a diffractive nonlinear Kerr medium with anomalous dispersion

Kerr media are applied in the photonic lattices and optical fibers, while optical fiber communication becomes one of the main pillars of modern communication. In this letter, we study a (3 + 1)-dimensional nonlinear Schrodinger equation with distributed coefficients for the spatiotemporal optical solitons or light bullets in a diffractive nonlinear Kerr medium with anomalous dispersion. The N-dark soliton solutions in terms of the Gramian is obtained via the Kadomtsev-Petviashvili hierarchy reduction, where N is a positive integer. Via the graphic analysis, we observe the interaction of the two dark solitons. Effects from the diffraction/dispersion coefficient beta(z) and gain coefficient gamma(z) are also discussed on the amplitudes and oscillations of the two dark solitons, as well as on the interaction of the two dark parabolic shape solitons.