Asymptotics of solutions to the generalized Ostrovsky equation

We consider the Cauchy problem for the generalized Ostrovsky equationutx=u+(f(u))xx,utx=u+(f(u))xx, where f(u)=|u|ρ−1uf(u)=|u|ρ−1u if ρ   is not an integer and f(u)=uρf(u)=uρ if ρ   is an integer. We obtain the L∞L∞ time decay estimates and the large time asymptotics of small solutions under suitable conditions on the initial data and the order of the nonlinearity.