The Korteweg-de Vries equation and beyond (Q1896400)

The author reviews a new method for linearizing the initial-boundary value problem of the Korteweg-de Vries (KdV) equation on the semi-infinite line for decaying initial and boundary data. The author also presents a novel class of physically important integrable equations. These equations, which include generalizations of the KdV, of the modified KdV, of the nonlinear Schrödinger and of the \(N\)-wave interactions, are as generic as their celebrated counterparts and it appears that they describe certain physical situations more accurately.