Linear spectral problems, non-linear equations and the δ-method

It is known that a number of non-linear partial differential equations and systems can be linearised, in principle, by solving an inverse scattering problem for an associated linear equation or system. The formal inverse scattering problem in one or several dimensions can generally be formulated precisely as a delta -problem. The authors concentrate on the delta method and the closely related features of the inverse scattering transform.