Modified reduced Ostrovsky equation: Integrability and breaking

Abstract

The modified reduced Ostrovsky equation is a reduction of the modified Korteweg-de Vries equation, in which the usual linear dispersive term with a third-order derivative is replaced by a linear nonlocal integral term, representing the effect of background rotation. Here we study the case when the cubic nonlinear term has the same polarity as the rotation term. This equation is integrable provided certain slope constraints are satisfied. We demonstrate, through theoretical analysis and numerical simulations, that when this constraint is not satisfied at the initial time, wave breaking inevitably occurs.