On progress in constructing explicit solutions in inverse scattering theory

Abstract: Inverse scattering theory is a final step of the well known inverse scattering transform method. It does not represent difficulties in 1+1 models but becomes much more complicated for  1+2 models. We were able to reach a significant progress in constructing explicit solutions for Novikov-Veselov, Kadomtsev-Petviashvili-II and Davey-Stewartson-II (focusing) equations.