Computer algebra, Painlevé analysis and the time-dependent-coefficient nonlinear Schrödinger equation

The variable-coefficient nonlinear Schrödinger equations describe certain physical systems with nonuniform backgrounds. In this paper, the application of the Painlevé analysis and computer algebra leads to an auto-Bäcklund transformation and some special solutions to a general time-dependent coefficient version of the nonlinear Schrödinger equation.