An innovative multivariate method for exploring soliton dynamics in nonlinear models

This article presents the multivariate generalized exponential rational integral function method (MGERIFM) for addressing the (1+1)-dimensional generalized Kundu-Eckhaus equation (GKEE). Based on the generalized exponential rational function framework, the MGERIF exhibits efficacy in formulating solutions associated with trigonometric, exponential, and hyperbolic functions. The findings obtained from the MGERIFM have substantial relevance in multiple scientific disciplines, including nonlinear optics, fluid dynamics, and plasma physics. To clarify the physical significance of the solutions produced, we employ 3D surface graphs, contour plots and line plots, exploring a range of parameter choices. The application of this visualization technique enhances our understanding of the solutions obtained and facilitates a thorough discussion about their potential applications in practical situations. By employing the MGERIFM, we refine approaches to tackle integrable systems, thereby establishing a robust basis for exploring the intricate domain of nonlinear phenomena across various physical contexts.