Scattering transformation at fixed non-zero energy for the two-dimensional Schrödinger operator with potential decaying at infinity (Q2759251)

This paper considers the problem of reconstructing the potential of a two dimensional Schrödinger operator from scattering data at fixed energy. This problem is equivalent to the fixed frequency inverse scattering acoustic problem, and hence, the results apply in both cases. As this problem possesses an infinite-dimensional symmetry algebra, generated by the Novikov-Veselov hierarchy, it is in some sense exactly soluble. The author gives a detailed review of results obtained by himself and by other authors. The methods of modern soliton theory are heavily used.