  We consider the initial-value problem for the regularized
Boussinesq-Ostrovsky equation in the class of periodic functions. Validity of
the weakly-nonlinear solution, given in terms of two counter-propagating waves
satisfying the uncoupled Ostrovsky equations, is examined. We prove
analytically and illustrate numerically that the improved accuracy of the
solution can be achieved at the time scales of the Ostrovsky equation if
solutions of the linearized Ostrovsky equations are incorporated into the
asymptotic solution. Compared to the previous literature, we show that the
approximation error can be controlled in the energy space of periodic functions
and the nonzero mean values of the periodic functions can be naturally
incorporated in the justification analysis.
