Approximate solutions of bright and dark optical solitons in birefrigent fibers

In this article, the residual power series method (RPSM) for solving the nonlinear Schrödinger equation is introduced. Residual power series algorithm gets Maclaurin expansion of the numerical soliton solutions to birefringent fibers. Dark and singular numerical optical soliton solutions are listed for these nonlinearities. We studied these cases as an application for the nonlinear Schrödinger equation. Then we have provided a numerical study of the effect of changing the bright and dark soliton parameters. The solutions of our equation are computed in the form of rabidly convergent series with easily calculable components by using mathematica software package. Reliability of the method is given graphical consequens and series solutions are made use of to illustrate the solution. The found consequens show that the method is a power and efficient method in determination of solution the nonlinear Schrödinger equation.