Analytical localized wave solutions of the generalized nonautonomous nonlinear Schrödinger equation with Gaussian shaped nonlinearity

We construct analytical localized wave solutions to the generalized nonautonomous nonlinear Schrödinger equation with Gaussian shaped nonlinearity and trapping potentials by using a similarity transformation technique. Our results show that analytical localized wave solutions possess n−1n−1 zeros where their existence requires some restrictive conditions corresponding to the dispersion coefficient, the Gaussian shaped nonlinearity, the gain (loss) coefficient, and the trapping potential. In addition, the stability analysis of the solutions is discussed numerically.