Wave interactions and structures of (4+1)-dimensional Boiti-Leon-Manna-Pempinelli equation

This article characterizes nonlinear wave propagation in an incompressible fluid by investigating an exact unique solution of the (4+1)-dimensional Boiti-Leon-Manna-Pempinelli (BLMP) equation. A novel condition assertion for a polynomial function in a linear or a nonlinear combinations of the functions form simplifies the solution formulation for the (4+1) BLMP equation. This approach is used to create a new (1) Multiple-lump wave solution, (2) Stripe soliton solutions, (3) Breather profile, (4) Mixed solution of lump wave and soliton, (5) Mixed lump-kink waves and interaction, (6) Interaction solutions between lump wave and solitary waves, etc. By utilizing four powerful ansatz function techniques, above different wave structures of the solution of the BLMP equation and corresponding wave interaction phenomena are obtained. The physical phenomena for these solutions are analyzed by studying the influence of the parameters for these solutions. The representative solution 3D and contour plots corresponding to specified arbitrary functions in the solutions are given, which provide physical insight into the structure of the solution. This study can help to understand physical phenomena in many areas of applied physics, especially nonlinear optics and acoustics waves.