Nonlocal symmetries and interaction solutions of the Benjamin-Ono equation

The nonlocal symmetries for the Benjamin-Ono equation are obtained with the truncated Painlevé method. The nonlocal symmetries can be localized to the Lie point symmetries by introducing auxiliary dependent variables. The finite symmetry transformations related to the nonlocal symmetries are computed. The Benjamin-Ono equation is proved to be consistent Riccati solvable and many interaction solutions among solitons and other types of nonlinear excitations can be obtained by means of the consistent tanh expansion method with arbitrary constants.