Abstract: Based on the WTC method and the symbolic computation, the Painlevé analysis and exact solutions of the variable coefficient nonlinear Schr?dinger (NLS) equation which involves four arbitrary functions of space-time. Among the four variable coefficients of the equation, the first two are two order dispersion of longitudinal distance and nonlinear coefficient respectively, and the last two are the real and imaginary parts of the optical fiber loss factor. At first, some parametric restriction of four variable coefficients are derived to pass Painlevé test with the WTC method. Then, three special forms of rational function solutions are derived with the Painlevé truncation method. At the same time, some other type solutions are obtained by the variable separation method. The obtained results is the extension of the existing conclusions.

Key words: WTC method