A study of propagation of the ultra-short femtosecond pulses in an optical fiber by using the extended generalized Riccati equation mapping method

摘要

Abstract In this study, the propagation of the ultra-short femtosecond pulses in an optical fiber is modeled by the Kundu–Eckhaus equation with cubic, quintic nonlinearities, and the Raman effect. The Kundu–Eckhaus equation is a special class of nonlinear Schrödinger equation. To find optical soliton solutions, the extended generalised Riccati equation mapping method is applied. The Kundu–Eckhaus equation is a special class of nonlinear Schrödinger equation. To find optical soliton solutions, the extended generalized Riccati equation mapping method is applied. The generalized Riccati equation mapping method is used in conjunction with the (G′/G)documentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$(G'/G)$$end{document}-expansion method, which is known for its high accuracy and ability to construct exact solutions for a variety of nonlinear partial differential equations. The obtained solutions provide an sound explanation of the propagation of ultra-short femtosecond pulses in an optical fibers. The discovered solutions are illustrated graphically through 3D and contour graphs using Matlab.