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[Formula: see text]+[Formula: see text]1)-dimensional nonlinear Schrödinger 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 [Formula: see text] and gain coefficient [Formula: see text] 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.
Analytical and approximate solutions of nonlinear Schrödinger equation with higher dimension in the anomalous dispersion regime
