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

Abstract

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