Invariance analysis for determining the closed-form solutions, optimal system, and various wave profiles for a (2+1)-dimensional weakly coupled B-Type Kadomtsev-Petviashvili equations

• The optimal system of Lie subalgebra is employed to analyze weakly coupled B-type Kadomtsev-Petviashvili equations. • We started with Lie infinitesimals, potential vector fields, and a one-dimensional optimal system. • Symmetry reductions are applied to obtain various explicit solutions. • Various wave profiles are used to demonstrate the dynamics of several closed-form solutions. • In the field of advanced research and development, such investigations are fully supported. In the case of negligible viscosity and surface tension, the B-KP equation shows the evolution of quasi-one-dimensional shallow-water waves, and it is growingly used in ocean physics, marine engineering, plasma physics, optical fibers, surface and internal oceanic waves, Bose-Einstein condensation, ferromagnetics, and string theory. Due to their importance and applications, many features and characteristics have been investigated. In this work, we attempt to perform Lie symmetry reductions and closed-form solutions to the weakly coupled B-Type Kadomtsev-Petviashvili equation using the Lie classical method. First, an optimal system based on one-dimensional subalgebras is constructed, and then all possible geometric vector yields are achieved. We can reduce system order by employing the one-dimensional optimal system. Furthermore, similarity reductions and exact solutions of the reduced equations, which include arbitrary independent functional parameters, have been derived. These newly established solutions can enhance our understanding of different nonlinear wave phenomena and dynamics. Several three-dimensional and two-dimensional graphical representations are used to determine the visual impact of the produced solutions with determined parameters to demonstrate their dynamical wave profiles for various examples of Lie symmetries. Various new solitary waves, kink waves, multiple solitons, stripe soliton, and singular waveforms, as well as their propagation, have been demonstrated for the weakly coupled B-Type Kadomtsev-Petviashvili equation. Lie classical method is thus a powerful, robust, and fundamental scientific tool for dealing with NPDEs. Computational simulations are also used to prove the effectiveness of the proposed approach.