Nonautonomous solitons in parity-time symmetric potentials

Some analytical solutions of a (1+1)-dimensional nonlinear Schrödinger equation with inhomogeneous diffraction and nonlinearity in the presence of the parity-time symmetric potential are derived. All characteristic parameters such as amplitudes, speeds and widths of solutions are adapted both to the diffraction and to nonlinearity variations. The dynamical behaviors of two kinds of nonautonomous solitons with different parity-time symmetric potentials are investigated respectively both in the exponential diffraction decreasing waveguide and in the periodic modulated system. Moreover, phase changes for two kinds of nonautonomous solitons are illustrated in detail. These results may provide alternative methods in potential applications of synthetic parity-time symmetric systems.