Exact and numerical solutions of the generalized breaking soliton system: Insights into non-linear wave dynamics

In this paper, we examined the (2+1)-dimensional generalized breaking soliton system (GBSS), an adaptable framework that accurately describes the three-dimensional, wave-dominated interactions occurring in many non-linear media, i.e., fluids, plasmas, and optical fibers. We used an improved F-expansion technique to generate new families of exact solitonic and periodic wave solutions, significantly enlarging the well-studied solution space and providing insight into the complicated interaction between multi-pulse solitons. Validation of these results and an assessment of their stability were carried out by developing a numerical scheme based on finite difference and undertaking a detailed error and stability analysis, demonstrating unconditional stability across a range of parameter values. The results provide new insights into the interplay of dispersion, non-linearity, and cross-wave coupling in governing soliton formation and energy transport in multidimensional systems. In addition to its theoretical importance, this work can provide valuable practical information on engineering applications such as soliton-based communications and wave control applications in fluid systems. This study offers a new methodology to investigate more complex non-linear wave phenomena by integrating the power of symbolic computation with that of robust numerical verification, opening new opportunities for further developments in soliton-driven technologies.