(3+1)-dimensional Gaussian-type solitons in the quintic-septimal nonlinear parity–time symmetric media. (6th June 2019) - Chen, Yi-Xiang; Xiao, Xiao; Xu, Fang-Qian
Abstract: We analyze (3+1)-dimensional constant-coefficient and variable-coefficient quintic-septimal nonlinear Schrödinger 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 the 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 the powers and power-flow densities of the soliton solution illustrate that the powers flow from the gain region to the loss region. Based on solutions of the 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 phase-switch phenomenon is found.