## Analytical solitary-wave solutions of the generalized nonautonomous cubic-quintic nonlinear Schroedinger equation with different external potentials

A large family of analytical solitary wave solutions to the generalized nonautonomous cubic-quintic nonlinear Schroedinger equation with time- and space-dependent distributed coefficients and external potentials are obtained by using a similarity transformation technique. We use the cubic nonlinearity as an independent parameter function, where a simple procedure is established to obtain different classes of potentials and solutions. The solutions exist under certain conditions and impose constraints on the coefficients depicting dispersion, cubic and quintic nonlinearities, and gain (or loss). We investigate the space-quadratic potential, optical lattice potential, flying bird potential, and potential barrier (well). Some interesting periodic solitary wave solutionsmore »