Dispersive soliton solutions to the (4+1)-dimensional Boiti-Leon-Manna-Pempinelli equation via an analytical method

The primary objective of this study is to extract nonlinear wave patterns from the (4+1)-dimensional Boiti-Leon-Manna-Pempinelli (4D-BLMP) equation, considering both constant and time-dependent coefficients, which is used widely to describe the incompressible fluid. By employing the amended extended tanh-function method, we successfully obtained innovative solutions in the form of combo dark bright, hyperbolic or lumps, periodic, and singular mix solitons solutions, and others. To ensure the utmost precision and reliability of our findings, we rigorously confirm them using the robust Mathematica software. These solutions hold paramount importance in the domains of in the study of incompressible fluids and acoustic waves, enriching our understanding of the foundational physical principles embedded within the equation. The study visually presents the computed wave solutions using 2D, 3D, and contour plots, effectively representing the internal structure of the phenomenon. This study proves that the computational method used is efficient, brief, and widely applicable, making it valuable to engineers who work with engineering models and dynamical models. This research can help to better understand physical phenomena in many areas of applied physics, particularly in the study of incompressible fluids and acoustic waves.