THE SMALL DISPERSION LIMIT OF THE BENJAMIN-ONO-EQUATION AND THE EVOLUTION OF A STEP INITIAL CONDITION

The solution of the Benjamin-One equation is presented for a step init ial condition. This solution models the evolution of an internal bore wave in deep fluids. The Whitham modulation theory is used to construc t the asymptotic solution which provides an accurate description of th e wave evolution in the small dispersion limit. It is shown that the i nitial step profile evolves into a train of solitary waves and the tot al number of created solitary waves increases without limit in proport ion to time. The amplitude of the leading solitary wave is then found to be four times the amplitude of the initial step.