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Exact analytical solutions to the nonlinear Schrödinger equation model

A method is developed for constructing a series of exact analytical solutions of the nonlinear Schrödinger equation model (NLSE) with varying dispersion, nonlinearity, and gain or absorption. With the help of symbolic computation, a broad class of 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 investigated.