Gaussian-type light bullet solutions of the (3+1)-dimensional Schrödinger equation with cubic and power-law nonlinearities in PT-symmetric potentials

Two kinds of Gaussian-type light bullet (LB) solutions of the (3+1)-dimensional Schrödinger equation with cubic and power-law nonlinearities in PT-symmetric potentials are analytically obtained. The phase switches, powers and transverse power-flow densities of these solutions in homogeneous media are studied. The linear stability analysis of these LB solutions and the direct numerical simulation indicate that LB solutions are stable below some thresholds for the imaginary part of PT-symmetric potentials in the defocusing cubic and focusing power-law nonlinear medium, while they are always unstable for all parameters in other media. Moreover, the broadened and compressed behaviors of LBs in the exponential periodic amplification system and diffraction decreasing system are discussed. Results indicate that LB is more stable for the sign-changing nonlinearity in the exponential periodic amplification system than for the non-sign-changing nonlinearity in the diffraction decreasing system at the same propagation distances.