Initial-value problem for coupled Boussinesq equations and a hierarchy of Ostrovsky equations

► We consider the initial-value problem for coupled Boussinesq equations. ► Hierarchy of Ostrovsky equations is derived for unidirectional waves by averaging. ►Nonsecular weakly nonlinear solution is constructed. ► Numerical simulations support our theory. ► Solution for the single Boussinesq equation is obtained as a particular case.