In the fields of NLPDEs, or nonlinear partial differential equations, are used in research and engineering are essential. They were employed to describe a variety of occurrences by simulating complex interactions and correlations between variables. These equations are used in many scientific fields, such as quantum physics, mathematical biology, fluid dynamics, and materials science [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]. By resolving NLPDEs, scientists can generate predictions, get important insights, and provide original solutions to issues that arise in the actual world. Consequently, a number of techniques are created to find precise solutions for NLPDEs. The modified extended direct algebraic methodology [25, 26, 27, 28, 29, 30], the extended F-expansion technique [31], the modified extended mapping technique [32], the Riccati equation mapping technique [33], and the Kudryashov approach [34] are some of these techniques. Wave packets that are able to sustain themselves while travelling and keep their shape and speed are referred to as solitary waves, or solitons [35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45].These solitary waves can occur in multiple modes in multi-mode fibres, each with unique properties. Solitary waves are created as a result of complex nonlinear dynamics resulting from the interaction between the modes. These solitary waves are a promising field for study in nonlinear optics and fibre optics because they can display complex behaviours like fission, fusion, and collision. For instance, Zhou et al. [46] examined the features of multimode fibre propagation of soliton pulses and demonstrated how to efficiently control optical soliton properties. Additionally, they demonstrated how parameter selection can be used to influence soliton properties. According to research by Deng et al. [47], multimode soliton interactions in graded index optical fibres cause the trailing soliton, which then runs into the front-running soliton. Sun and others [48] offered understanding of the intricate dynamics of nonlinear graded-index solitons in multimode fibres and advances knowledge in this regard of their behavior. et al. Mayteevarunyoo [49]. created the dispersion management (DM) in a multimode system for three-dimensional (3D) solitons fibre optic. It is found that the parameter for DM strength influences quasi-stability in the three-dimensional spatiotemporal solitons noticed at reduced concentrations, and total stability at increased values. The research also looked at 3Dsolitons colliding, demonstrating quasielastic relationships. The propagation of a nonlinear localized wave via a multimode fiber is described by a CHNLSE that reads as [50]: