On Approximate Solutions of Bright Optical Soliton for Schrodinger Equation of Power Law Nonlinearity

Abstract

In this work, the residual power series method (RPSM) and homotopy analysis transform method (HATM) for solving Schrodinger equation of power law nonlinearity is introduced. Residual power series algorithm gets Maclaurin expansion of the numerical soliton solutions. The HATM is a combined form of the Laplace transform method and homotopy analysis method. 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 methods are given graphical consequence and series solutions are made use of to illustrate the solution. The approximate solutions are compared with the known exact solutions. The found consequence show that these methods are very power and efficient in determination of bright optical soliton of nonlinear Schrodinger equation and can be applied to other nonlinear problems.