Soliton deflexion for(1 + 3)D Kadomtsev-Petviashvili Equation

Two types of soliton deflexion of (1 + 3)D Kadomtsev–Petviashvili (K–P) equation are considered. Using the Hirota bilinear form and the new technique of “homoclinic test”, a type of exact periodic soliton solution of the K–P equation with positive transverse dispersion effects is obtained. Another type of periodic soliton solution is found by means of the periodic soliton solution of the K–P equation with negative transverse dispersion effects and a temporal and spatial transformation. It is also investigated that the equilibrium solution u 0 = - 1 6 is an unique deflexion point, periodic soliton of traveling in different spatial directions will be interchanged with the solution varying from one side of - 1 / 6 to the other side.