Flat coordinates and integrable dispersive Hamiltonian systems

In the framework of hydrodynamic type systems the concept of “flat coordinates” was introduced by B.A.Dubrovin and S.P.Novikov in 1983 year. Nevertheless, this concept can be naturally extended to dispersive nonlinear systems. Classical example: two-dimensional Gelfand–Dickey reductions of the three-dimensional Kadomtsev–Petviashvili hierarchy.