The Schrodinger equation and a multidimensional inverse scattering transform

The Schrodinger equation is one of the most important equations in mathematics, physics and also engineering. We outline some connections between transformations of non-linear equations, the Schrodinger equation and the inverse scattering transform. After some remarks on generalizations into higher dimensions we present a multidimensional partial derivative method based on Clifford analysis. To explain the method we consider the formal solution of the inverse scattering problem for the n-dimensional time-dependent Schrodinger equations given by A.I. Nachman and M.J. Ablowitz. Copyright (C) 2002 John Wiley Sons, Ltd.