Spatiotemporal modulated solitons in a quasi-one-dimensional spin-1 Bose–Einstein condensates

In this paper, we investigate the nonautonomous bright/dark solitons in a quasi-one-dimensional spin-1 Bose–Einstein condensates through a three coupled Gross–Pitaevskii (GP) system with space–time-dependent external potential and temporally modulated gain/loss distributions. Based on the Hirota bilinear method, we analytically construct the bright soliton solutions when the coupled GP system exhibits attractive interactions, while we obtain the dark soliton solutions when the coupled GP system exhibits repulsive interactions. The influence of spatiotemporal modulated external potentials, such as the gain/loss distribution Γ(t), on bright/dark soliton dynamics is analyzed in detail via the analytical solutions. By taking different Γ(t), we obtain different types of bright solitons, including periodic, dromion-like and parabolic solitons, and also derive dark solitons on different backgrounds, such as periodic, parabolic and kink backgrounds. We analyze the regulatory effects of different wavenumber ratios on the attraction and squeezing of bound-state solitons. Through the asymptotic analysis, we find that the interactions between two solitons are elastic. In addition, we conduct research on the forward and inverse problems of the above results via the parallel hard-constraint physical informed neural network (phPINN) method. The predicted solitons and potential functions are in good agreement with the exact solitons and potential in the system.