Abundant closed-form wave solutions and dynamical structures of soliton solutions to the (3+1)-dimensional BLMP equation in mathematical physics

Abstract

Abstract The physical principles of natural occurrences are frequently examined using nonlinear evolution equations (NLEEs). Nonlinear equations are intensively investigated in mathematical physics, ocean physics, scientific applications, and marine engineering. This paper investigates the Boiti-Leon-Manna-Pempinelli (BLMP) equation in (3+1)-dimensions, which describes fluid propagation and can be considered as a nonlinear complex physical model for incompressible fluids in plasma physics. This four-dimensional BLMP equation is certainly a dynamical nonlinear evolution equation in real-world applications. Here, we implement the generalized exponential rational function (GERF) method and the generalized Kudryashov method to obtain the exact closed-form solutions of the considered BLMP equation and construct novel solitary wave solutions, including hyperbolic and trigonometric functions, and exponential rational functions with arbitrary constant parameters. These two efficient methods are applied to extracting solitary wave solutions, dark-bright solitons, singular solitons, combo singular solitons, periodic wave solutions, singular bell-shaped solitons, kink-shaped solitons, and rational form solutions. Some three-dimensional graphics of obtained exact analytic solutions are presented by considering the suitable choice of involved free parameters. Eventually, the established results verify the capability, efficiency, and trustworthiness of the implemented methods. The techniques are effective, authentic, and straightforward mathematical tools for obtaining closed-form solutions to nonlinear partial differential equations (NLPDEs) arising in nonlinear sciences, plasma physics, and fluid dynamics.