On the limit from the intermediate long wave equation to the Benjamin–Ono equation

The intermediate long wave equation is a physically important singular integrodifferential equation containing a parameter, referred to here as δ. For δ → ∞ it reduces to the Benjamin–Ono equation. It has been recently shown that the inverse scattering transform schemes of the above equations have certain significant differences. Here it is shown that for δ → ∞, the inverse scattering transform scheme of the intermediate long wave equation reduces to that of the Benjamin–Ono equation.