A method is developed for constructing a series of exact nalytical solutions of the nonlinear Schr\"{o}odinger equation model (NLSE) with varying dispersion, nonlinearity, and gain or absorption. With the help of symbolic computation, rich exact analytical solutions of NLSE are obtained. From our results, many previous known results of NLSE obtained by some authors can be recovered by means of some suitable selections of the arbitrary functions and arbitrary constants. Further, the formation, interaction and stability of solitons have been investigatied.