New interaction solutions of Kadomtsev-Petviashvili equation

The residual symmetry coming from truncated Painleve expansion of KP equation is nonlocal, which is localized in this paper by introducing multiple new dependent variables. By using the standard Lie group approach, the symmetry reduction solutions for KP equation is obtained based on the general form of Lie point symmetry for the prolonged system. In this way, the interaction solutions between solitons and background waves is obtained, which is hard to study by other traditional methods.