Nonautonomous cnoidal wave and soliton management in parity-time symmetric potentials

We obtain (1 + 1)-dimensional analytical nonautonomous cnoidal waves and solitons and (2 + 1)-dimensional nonautonomous soliton of the nonlinear Schrِdinger equations with inhomogeneous diffraction and nonlinearity in presence of the parity-time symmetric potentials. The dynamical behaviors of (1 + 1)-dimensional nonautonomous cnoidal waves and solitons in the exponential and hyperbolic diffraction decreasing waveguides with the self-focusing and self-defocusing nonlinearities are studied, respectively. Dynamical characteristics of form factors including the amplitude, width, and phase change are analyzed. The comparison of the dynamical behaviors of nonautonomous cnoidal waves and solitons in the exponential and hyperbolic diffraction decreasing waveguides are investigated. Moreover, the compression of (2 + 1)-dimensional nonautonomous soliton is also discussed.