Sub-picosecond pulses in single-mode optical fibres with the Kaup–Newell model via two innovative methods

This work aims to explore the optical solitons of the Kaup–Newell model (KNM) which describes the glamorous technology of sub-picosecond pulses that spread via single-mode optical fibres using two innovative methods, namely Wang’s Bäcklund transformation-based method (WBTBM) and Wang’s direct mapping method (WDMM). Different kinds of exact solutions expressed in the form of the rational function, Exp function, sin–cos function, sinh–cosh function, hyperbolic function (sech function and csch function) and trigonometric function (sec function and csc function) are obtained, which include the bright soliton, dark soliton, singular soliton and other travelling wave solutions. To reveal the dynamic behaviours of the different solutions, the 3D plots, 2D contours and 2D curves are drawn with the help of the Mathematica software. The findings in this work confirm that the mentioned methods are effective, straightforward and powerful, and can be used to handle other partial differential equations (PDEs) arising in the optics.