Lumps, solitons, modulation instability and stability analysis for the novel generalized (2+1)-dimensional nonlinear model arising in shallow water

In this study, the (2+1)-dimensional Kadomtsev–Petviashvili type equation is investigated that describes the nonlinear wave patterns of behavior and properties in oceanography, fluid dynamics, and shallow water. Firstly, the Hirota bilinear form is implemented to develop a variety of lump, strip soliton and periodic waves solutions for the governing model. Furthermore, some interesting traveling and semi-analytical solitons are generated by availing the extended modified auxiliary equation mapping technique and the Adomian decomposition algorithm. Moreover, in order to determine the absolute error, we have constructed a juxtapose of approximate and soliton results. Additionally, we deliberate the stability analysis and the modulation instability for the governing model extensively to validate the scientific computations. Moreover, the graphical portrayals which include contour plots, 2D and 3D models are illustrated that are useful for understanding the behaviors and dynamics presented by the model’s solutions. The findings of current study are quite novel and make a big contribution to soliton dynamics and mathematical physics.