Types of solutions of the variable-coefficient nonlinear Schrodinger equation with symbolic computation

By using Hirota's bilinear method and symbolic computation, solutions for a variable-coefficient nonlinear Schrodinger equation are obtained theoretically. It is found that the type of the solutions changes with the different choices of the group-velocity dispersion coefficient beta(2)(z). According to those solutions, the relevant properties and features of physical and optical interest are illustrated. In addition, an effective technique for controlling the shape of the pulses is presented. The results of this paper will be valuable to the study of the future development of ultrahigh rate and long-distance optical communication systems.