Stable light-bullet solutions in the harmonic and parity-time-symmetric potentials

Analytical light-bullet solutions of a ($3+1$)-dimensional nonlinear Schr\"odinger equation with inhomogeneous diffraction or dispersion and nonlinearity in the presence of the harmonic and parity-time-symmetric potentials are explored. Diffraction or dispersion and nonlinearity play important roles in the evolutional characteristics such as amplitude, width, and phase. The compression and broadening behaviors of light bullets are discussed and compared in the exponential, Gaussian and hyperbolic diffraction or dispersion decreasing media and the periodic distributed amplification system. Moreover, phase changes of light bullets in different systems are also illustrated.