Theoretical study of resonance of the Kadomtsev–Petviashvili equation

As is well known, Korteweg–de Vries equation is a typical one which has planar solitary waves. By considering the higher-dimensional nonlinear waves, we studied a Kadomtsev–Petviashvili (KP) equation and found some interesting results which explain experimental results well enough. Two same amplitude soliton solution of KP equation explain resonance phenomena reported by some experiments. Two arbitrary amplitude soliton solution of KP equation is also obtained in this Letter, which can also results in resonance phenomena. The phase shift after interaction between two soliton are obtained theoretically in this Letter. It is in agreement with experimental results. [Copyright &y& Elsevier]