Exact wave solutions of new generalized Bogoyavlensky–Konopelchenko model in fluid mechanics

In this paper, we examine a novel generalized Formula: see text-dimensional Bogoyavlensky–Konopelchenko (gBK) model analytically via application of five mathematical methods, namely called Extended Simple Equation (ESE) method, Modified Extended Auxiliary equation mapping (MEAEM) method, Formula: see text-expansion method, Formula: see text-expansion method and modified F-expansion method, respectively, to obtain different types solitary wave solutions in the form of trigonometric, hyperbolic, rational and exponential functions as compared to solutions exist in S. T. Chen and W. X. Ma, Math. China 13 (2018) 525; A. Sonia, A. Jamshad, S.-U. Rehman and A. Ali, Int. J. Appl. Comput. Math. 9 (2023). The research focuses on physical systems, physiology, mathematical applications, engineering fields, and the chemical processes of species in the porous nanoparticles, examining the impact of various parameters on the nonlinear model. The graphs of some solutions are plotted in the form of two-dimensional and three-dimensional by assigning the particular values to the paraments with the assistance of mathematica software which illustrated the physical behavior of the concern model. The derived solution has numerous applications in fluid dynamics and the interaction of Riemann waves and long waves.