The study of the Korteveg–de Vries (KdV) equation is considered as a special chapter of potential scattering where the dynamic scattering equation is a set of coupled “Lax” equations. With this approach, all points of view and all tools of potential scattering have their counterpart in the standard inverse scattering transform, which appears as a straightforward consequence. If the approach is transposed to the quarterplane problem, it shows a generalization to KdV of the solutions obtained by Fokas in the linearized KdV problem, but unfortunately the last step is iterative and complicated. The method can also be used to study NLS.