Abstract
Abstract The Hirota bilinear method is prepared for searching the diverse soliton solutions to the (2+1)-dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony (KP-BBM) equation. Also, the Hirota bilinear method is used to find the lump and interaction with two stripe soliton solutions. Interaction among lumps, periodic waves, and one-kink soliton solutions are investigated. Also, the solitary wave, periodic wave, and cross-kink wave solutions are examined for the KP-BBM equation. The graphs for various parameters are plotted to contain a 3D plot, contour plot, density plot, and 2D plot. We construct the exact lump and interaction among other types of solutions, by solving the underdetermined nonlinear system of algebraic equations with the associated parameters. Finally, analysis and graphical simulation are presented to show the dynamical characteristics of our solutions, and the interaction behaviors are revealed. The existing conditions are employed to discuss the available got solutions.
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