The (3+1)-dimensional Boussinesq equation: Novel multi-wave solutions

The Boussinesq equation is a partial differential equation that describes the behavior of waves in shallow water. In this paper, we address some new dynamical behaviors to the (3+1)-dimensional Boussinesq equation, which are not constructed beforehand. Various solutions namely: multi-soliton, multi-M-lump, and the hybrid soliton solutions are reported. New explored features of equation are presented graphically to better analyze the gained solutions. For different period of time multi-soliton, multi-lump solutions are plotted. The results have important applications in oceanography, geophysics, fluid dynamics, and also used to study the behavior of waves in complex three-dimensional domains, particularly in situations where the nonlinear effects are strong.