Distinct models involving nonlinearity are mostly appreciated for illustrating intricate phenomena arise in the nature. The new (3+1)-dimensional generalized nonlinear Boiti-Leon-Manna-Pempinelli (BLMP) model describes the dynamical behaviors of nonlinear waves arise in incompressible fluid. This present effort deals with the well-known governing BLMP equation by adopting two efficient schemes, namely improved tanh and improved auxiliary equation. As a result, a variety of appropriate wave solutions are made available in different type functions. The gathered solutions are figured out to characterize their internal properties for depicting the relevant phenomena. Diverse wave profiles are noticed in 3D, 2D and contour sense after assigning parameter’s values involved in the achieved solutions. The finding results are comparably different and general due to the existing wave solutions. The employed approaches perform in a great way to construct analytic wave solutions of considered evolution equation and deserve further use in relevant research area.

Distinct models involving nonlinearity are mostly appreciated for illustrating intricate phenomena arise in the nature. The new (3 + 1)-dimensional generalized nonlinear Boiti-Leon-Manna-Pempinelli (BLMP) model describes the dynamical behaviors of nonlinear waves arise in incompressible fluid. This present effort deals with the well-known governing BLMP equation by adopting two efficient schemes, namely improved tanh and improved auxiliary equation. As a result, a variety of appropriate wave solutions are made available in different type functions. The gathered solutions are figured out to characterize their internal properties for depicting the relevant phenomena. Diverse wave profiles are noticed in 3D, 2D and contour sense after assigning parameter’s values involved in the achieved solutions. The finding results are comparably different and general due to the existing wave solutions. The employed approaches perform in a great way to construct analytic wave solutions of considered evolution equation and deserve further use in relevant research area. Mathematics Subject Classifications: 35C08, 35R11