New interaction solutions of the Kadomtsev-Petviashvili equation

The residual symmetry relating to the truncated Painlevé expansion of the Kadomtsev-Petviashvili (KP) equation is nonlocal, which is localized in this paper by introducing multiple new dependent variables. By using the standard Lie group approach, new symmetry reduction solutions for the KP equation are 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 are obtained, which are hard to find by other traditional methods.