The purpose of this paper is to study the breather waves, rogue waves and solitary waves of an extended (3 + 1)-dimensional Kadomtsev–Petviashvili (KP) equation, which can be used to depict many nonlinear phenomena in fluid dynamics and plasma physics.
The authors apply the Bell’s polynomial approach, the homoclinic test technique and Hirota’s bilinear method to find the breather waves, rogue waves and solitary waves of the extended (3 + 1)-dimensional KP equation.
The results imply that the extended (3 + 1)-dimensional KP equation has breather wave, rogue wave and solitary wave solutions. Meanwhile, the authors provide the graphical analysis of such solutions to better understand their dynamical behavior.
These results may help us to further study the local structure and the interaction of solutions in KP-type equations. The authors hope that the results provided in this work can help enrich the dynamic behavior of such equations.
