Two-dimensional nonautonomous solitons in parity-time symmetric optical media

An inhomogeneous nonlinear Schrödinger equation with diffraction and nonlinearity in the presence of the parity-time symmetric potential is studied, and 2D nonautonomous soliton family solutions are derived. The positive and negative signs in the phase bring about two kinds of abrupt phase transitions. Dynamical characteristics of form factors including the amplitude, width and phase are analyzed. The broadening and the compression of nonautonomous fundamental soliton are discussed. Moreover, the comparison of the dynamical behaviors of nonautonomous fundamental soliton in the diffraction decreasing waveguide with Gaussian, Logarithmic and hyperbolic profiles is investigated.