The Long-time asymptotic behaviour of the solutions of the Korteweg–de Vries equation.

The long-time whole asymptotic expausion of the “dispersion foil” of the KdV equation solutions is described and generalized wave operators are introduced. The saymptotic behaviour ot the Schrodinger equation solutions with the potential which has a type of KdV equation solutions is studied. It is shown KdV equation specifically connects with structure of the asymptotic behaviour of the Schrodinger equation solutions. As consequence the Known explicit formula is received for the main terms of Long-time asymptotic behaviour of the KdV equation solutions. The plan now to prove these results is ontliued.