LAUSR

We analyze the (3+1)-dimensional constant-coefficient and variable-coefficient quintic-septimal nonlinear Schr\"{o}dinger equations with dispersion/diffraction and parity-time symmetric potentials, and find exact Gaussian-type soliton solutions corresponding to two kinds of Gaussian-type parity-time symmetric potentials. From solutions of constant-coefficient equation in the homogeneous case, we know that the sign of the septimal nonlinearity coefficient is related to the highest order Gaussian parameter of the real component of parity-time symmetric potentials. The positive values for powers and power-flow densities of soliton solution illustrate that the powers flow from the gain region to the loss region. Based on solutions of variable-coefficient equation in the inhomogeneous case, the expansion and compression of (3+1)-dimensional Gaussian-type solitons are revealed in the periodic modulation system. Moreover, the phenomenon of the phase switch is reported.