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In this paper, by applying the Lie group method and the direct symmetry method, Lie algebras of the Benjiamin Ono equation are obtained, and we find that results of the two methods are same. Based on the Lie algebra, Lie symmetry groups, relationships between new solutions and old solutions, two kinds of ODEs as symmetry reductions are obtained. Making use of the power series method, the exact power series solution of the Benjiamin Ono equation has been derived. We also give the conservation laws of Benjiamin Ono equation by means of Ibragimovs new conservation Theorem.
Wang et al. (Sat,) studied this question.