摘要
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 1 spatial transformation method, respectively. The equilibrium solution uo =-1/6, a unique spatial-temporal bifurcation which is periodic bifurcation for KP-I and deflexion of soliton for KP-Ⅱ, is investigated.
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 1 spatial transformation method, respectively. The equilibrium solution uo =-1/6, a unique spatial-temporal bifurcation which is periodic bifurcation for KP-I and deflexion of soliton for KP-Ⅱ, is investigated.
基金
Supported by the National Natural Science Foundation of China under Grant Nos 10361007 and 10661002, the Yunnan Natural Science Foundation （No 2004A0001M）, and The IMS, CUHK.
