Wave profile analysis of a couple of (3+1)-dimensional nonlinear evolution equations by sine-Gordon expansion approach

The (3+1)-dimensional Kadomtsev-Petviashvili and the modified KdV-Zakharov-Kuznetsov equations have a significant impact in modern science for their widespread applications in the theory of long-wave propagation, dynamics of shallow water wave, plasma fluid model, chemical kinematics, chemical engineering, geochemistry, and many other topics. In this article, we have assessed the effects of wave speed and physical parameters on the wave contours and confirmed that waveform changes with the variety of the free factors in it. As a result, wave solutions are extensively analyzed by using the balancing condition on the linear and nonlinear terms of the highest order and extracted different standard wave configurations, containing kink, breather soliton, bell-shaped soliton, and periodic waves. To extract the soliton solutions of the high-dimensional…