Nonlinear dynamic behaviors of the generalized (3+1)‐dimensional KP equation.

Under investigation in this article is a generalized (3+1)‐dimensional Kadomtsev–Petviashvili (KP) equation, which is usually used to describe nonlinear phenomena in fluid dynamics. First, multiple waves solutions of this considered equation by means of the linear superposition principle are constructed. Second, the parameters of this considered model control multiple waves solutions are being investigated. We find that the parameters mainly affect the wave shapes, amplitude, and bright/dark nature. Third, we apply a polynomial function to construct rational solutions and rogue wave solutions when the parameters contain in the polynomial function are equal to zero and nonzero, respectively. Finally, the obtained results are demonstrated graphically to illustrate the nonlinear dynamics behaviors of multiple, rational, and rogue wave solutions in fluid mechanics. [ABSTRACT FROM AUTHOR]