The IVP for the Benjamin–Ono equation in weighted Sobolev spaces II

In this work we continue our study initiated in Fonseca and Ponce (2011) [11], on the uniqueness properties of real solutions to the IVP associated to the Benjamin–Ono (BO) equation. In particular, we shall show that the uniqueness results established in Fonseca and Ponce (2011) [11], do not extend to any pair of non-vanishing solutions of the BO equation. Also, we shall prove that the uniqueness result established in Fonseca and Ponce (2011) [11] under a hypothesis involving information of the solution at three different times cannot be relaxed to two different times.