Two exact solutions for nonlinear Schrodinger equation with variable coefficients Based on F-expansion method

摘要

In order to solve the problem of the nonlinear effect with increasing of the power in fiber, the nonlinear Schrodinger equation has been built with the coefficients of the second-order dispersion, gain, and third-order nonlinear effect. The coefficients are changed periodically with the transmission distance. The method of this paper includes three steps. The first one is that the highest orders of the amplitude part and phase part are determined by F-expansion method. The second one is that the relationship of the coefficients is determined after the trial solution into the original equation. The third one is that the two exact solutions are obtained for the second-order dispersion coefficients with the types of sine and sinh function respectively. The results show that the intensity distributions of the optical solitons are similar to Gaussian function with lattice distribution for two types of sine and sinh function when the F function is replaced with dn (θ,m) function and m → 1.