Periodic Bifurcation and Soliton Deflexion for Kadomtsev--Petviashvili Equation

The spatial--temporal bifurcation for Kadomtsev--Petviashvili (KP) equations is considered. Exact two-soliton solution and doubly periodic solution to the KP-I equation, and two classes of periodic soliton solutions in different directions to KP-II are obtained using the bilinear form, homoclinic test technique and temporal and spatial transformation method, respectively. The equilibrium solution u₀=-1/6, a unique spatial--temporal bifurcation which is periodic bifurcation for KP-I and deflexion of soliton for KP-II, is investigated.