Lie analysis and nonlinear propagating waves of the (3 + 1)-dimensional generalized Boiti–Leon–Manna–Pempinelli equation

The (3+1)-dimensional generalized Boiti-Leon-Manna-Pempinelli equation, which describes the evolution of Riemann wave propagation in an in-compressible fluid along three mutually perpendicular axes, is investigated in this research article. The study encompasses the analysis of Lie symmetries, corresponding symmetry reductions, and conservation laws associated with the equation. The Lie symmetry method is employed to determine the infinitesimal generators of the considered equation. Furthermore, commutator table is generated, and symmetry groups corresponding to each infinitesimal generator are derived. By utilizing the similarity reduction technique, the original nonlinear partial differential equation is transformed into nonlinear ordinary differential equations. Then, generalized exp(−ϕ(ζ)) expansion technique is utilized to solve the reduced equations and estimate specific traveling wave solutions for the equation. Moreover, graphical representations are employed to illustrate the traveling wave solutions, employing suitable parameter values. Additionally, the multiplier approach is utilized to calculate conserved vectors for the equation under consideration.