Soliton solutions of the Caudrey–Dodd–Gibbon equation using three expansion methods and applications

The main purpose of this research is to develop some new exact soliton solutions of the Caudrey–Dodd–Gibbon (CDG) equation using the Exp function method, the (G′/G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(G^\prime /G)$$\end{document}-expansion method, and the improved (G′/G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(G^\prime /G)$$\end{document}-expansion method. Exact solutions are also sought for certain appropriate parameter values. These solutions are graphically depicted. For clarity of physical features, the 3D and 2D graphical representations of some solutions are also provided. For the wide group of researchers working in the fields of mathematics and mathematical physics, the findings are novel and exciting. The physical behavior of obtained solutions has also been captured in terms of plots for various values of the involved parameters. There is also a comparison of the specified equation's solution with different approaches. It is worth noting that physical illustrations will aid in predicting the internal structure of the equations under consideration. The obtained findings show that the proposed schemes are completely compatible.