Generalized KdV Equation: Novel Nature Oceanic, M-lump and Physical Collision Waves

The main idea of this study is to explore new features for the generalized (3+1)-dimensional Korteweg-De Vries problem. This equation may be used to model various physical processes in several domains, including nonlinear optics, oceanography, acoustic waves in plasma physics, and other areas where coupled wave dynamics are essential. The Hirota method and long-wave technique to reveal various wave solutions are under consideration. Complex N-soliton solutions, M-lump waves, and hybrid solutions between some types of soliton and M-lump solutions are offered. The obtained solutions are one-, two-, and three-M-lump waves and mixed soliton-lump, soliton-two-lump, and two-soliton-lump solutions. Also, one-soliton, two-soliton, three-soliton, and four-soliton solutions in complex form are offered. To better analyse and understand the propagation characteristics of these solutions, 3D and contour plots for gained solutions are drawn. As far as we know, these solutions are novel and have not been revealed. Since the KdV equation often describes shallow water waves with weakly nonlinear restoring forces, we are interested in the features that have yet to be studied.