Sech-type and Gaussian-type light bullet solutions to the generalized (3 $$+$$ + 1)-dimensional cubic-quintic Schrödinger equation in $$\varvec{\mathcal {PT}}$$ PT -symmetric potentials

Abstract

We study two kinds of the generalized (3 $$+$$ 1)-dimensional cubic-quintic Schrodinger equation in $$\mathcal {PT}$$ -symmetric potentials and obtain two families (sech-type and Gaussian-type) and four kinds of analytical light bullet (LB) solutions. The stability of these solutions is tested by the linear stability analysis and the direct numerical simulation. Results imply that sech-type LB solutions are unstable for all parameters only in the extended Rosen–Morse potentials. Sech-type and Gaussian-type LB solutions are both stable below some thresholds for the imaginary part of other $$\mathcal {PT}$$ -symmetric potentials in the defocusing cubic and focusing quintic medium, while they are always unstable for all parameters in other media. Moreover, we discuss the broadened and compressed behaviors of LBs in inhomogeneous hyperbolic system and periodic amplification system.