Optical Solutions of Schrödinger Equation Using Extended Sinh–Gordon Equation Expansion Method

Amna Irshad,Ilyas Khan,El-Sayed M Sherif,Naveed Ahmed,Syed Tauseef Mohyud-Din,Umar Khan

doi:10.3389/fphy.2020.00073

Abstract

In this paper, we investigated nonlinear Schrodinger equation(NLS) to extract optical soliton solutions by implementing Extended Sinh-Gordon equation expansion method(ShGEEM). Optical soliton solutions included bright, dark, combined bright-dark, singular soliton combined singular soliton solutions, singular periodic wave solutions. Comparison of our new results have been presented to results exist in literature. Also, graphical analysis presented with 3D and contour graphs to understand the physics of obtained solutions.

Highlights

In recent years, soliton propagation in non-linear optical fiber has become the most extensive topic of research in the field of non-linear sciences
The extended Sinh–Gordon equation expansion method provides a large variety of optical soliton solutions [24–29]
By means of the extended Sinh–Gordon equation expansion method, we found some new more generalized exact solutions

Summary

INTRODUCTION

Soliton propagation in non-linear optical fiber has become the most extensive topic of research in the field of non-linear sciences. NLS helps to provide exact soliton solutions in non-linear fiber optics. Our main focus is the study of NLS [22] This equation has large physical importance in non-linear optics. To study Equation (1), we consider the following wave transformation:. Applying the traveling wave transformation Υ (x, t) = (ζ ) , ζ = λ(x − μt), to Equation (6), we acquire the following form of non-linear ODE:. Equation (9) has the following set of solutions, by substituting different values for given parameters θ and r. To obtain the different wave solutions of non-linear partial differential equations (NPDEs), we consider the equation in the following form:. Step IV: Substituting the values of Å0, Åκ , Bκ , μ in Equations (19)–(22), we obtain the following wave solutions to the nonlinear Equation (16): N (ζ ) =.

Result

CONCLUSIONS

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