Exploring localized waves and different dynamics of solitons in (2 + 1)-dimensional Hirota bilinear equation: a multivariate generalized exponential rational integral function approach

This study introduces the multivariate generalized exponential rational integral function (MGERIF) approach for solving the Hirota bilinear problem in 2 + 1 dimensions. Motivated by the generalized exponential rational function method, MGERIF method proves to be a powerful tool for finding solutions involving exponential, trigonometric, and hyperbolic functions. The solutions we found using MGERIF method have important applications in different scientific domains, including nonlinear optics, plasma physics, fluid dynamics, mathematical physics, and condensed matter physics. To illuminate the physical significance of the derived solutions, we employ three-dimensional (3D) and contour plots, exploring various parameter choices. This visualization approach enhances our understanding of the obtained solutions and facilitates a comprehensive discussion on their potential applications in real-world phenomena. By employing MGERIF method, we contribute to the advancement of methodologies for solving integrable systems, offering a valuable framework for exploring the rich landscape of nonlinear phenomena in various physical contexts.