Investigating soliton dynamics: Contemporary computational and numerical approaches for analytical and approximate solutions of the CDG model

This investigation employs contemporary computational and numerical techniques to derive analytical approximate soliton solutions for the Caudrey–Dodd–Gibbon model, which represents a significant variation of fifth-order Korteweg–de Vries equation. Diverse are constructed, employing distinct formats such as exponential, trigonometric, hyperbolic functions. Simulations, including two-dimensional, three-dimensional, contour, polar, discrete plots, presented illustrate real-world behavior single soliton. Furthermore, these utilized evaluate essential conditions implementing proposed scheme. The agreement between computed is demonstrated through various techniques. These results unequivocally establish superiority methods solving nonlinear mathematical physics problems.