Resonant multiple soliton and rogue type multiple lump wave solutions of the modified KdV–KP equation

This study investigates the precise solutions of the (2+1)-dimensional modified KdV–KP equation. Resonant multiple soliton solutions are examined by first discussing the linear superposition principle and then exploring two scenarios to illustrate the wave profiles and behaviors using various graphical representations. Utilizing the (3-2-4) bilinear neural network model, numerous rogue-type multiple lump wave solutions are generated, including 1-lump wave, 3-lump wave, and 6-lump wave results through symbolic computation. Additionally, the physical structure and dynamical features of these solutions are elucidated through three-dimensional plots and density graphs.