Dynamics of spatiotemporal soliton solutions to a generalized nonlinear Schrödinger equation with inhomogeneous coefficients

In this paper, we study the dynamics of spatiotemporal soliton solutions to a generalized nonlinear Schrödinger equation with inhomogeneous coefficients in analytical and numerical forms. The characteristics and physical applications of the soliton solutions are investigated under different modulations of the coefficients depicting diffraction, potential, nonlinearity, source, and gain. We find that structures of these soliton solutions can be effectively manipulated by appropriately selecting the source term. Besides, the impact of gate effect on soliton propagation is investigated by employing the hyper-Gaussian and rectangle functions as diffraction coefficients. The results show that (i) the hyper-Gaussian modulation can be replaced by the rectangle modulation for large exponent and (ii) the solitons undergo a broadening in width and a sudden decrease in amplitude when passing through the gate functions. Our findings may have potential applications for the investigation of soliton control in the fields of nonlinear optics and Bose–Einstein condensations.