Exact travelling wave solutions for generalized (3+1) dimensional KP and modified KP equations

In this article, the generalized (3+1) dimensional Kadomtsev–Petviashvili (KP) and modified Kadomtsev–Petviashvili equations are explored, along with weak non-linearity, dispersion and disturbances which can demonstrate the expansion of surface water and prolonged waves in fluid dynamics. These models explain numerous nonlinear phenomena in the field of fluid dynamics, plasma physics and many more. Modified auxiliary equation method is implemented to derive analytic exact solutions for the governing equations. Some interesting and new travelling wave patterns have been observed. The obtained results include kink soliton, kinky periodic solitary wave, dark-bright soliton and periodic waves. Furthermore, graphical analysis is performed by selecting appropriate values of parameters in these solutions to explain the dynamic behavior of some different types of solitons. The proposed technique is well organized and proficient to discuss various KP-type equations physically.