  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.
