| Popis: |
We consider the inverse scattering problem for the two-dimensional Schrödinger equation at fixed positive energy. Our results include inverse scattering reconstructions from the simplest scattering amplitudes. In particular, we give a complete analytic solution of the phased and phaseless inverse scattering problems for the single-point potentials (of the Bethe-Peierls-Fermi-Zeldovich-Berezin-Faddeev type). Then we study numerical inverse scattering reconstructions from the simplest scattering amplitudes using the Riemann-Hilbert-Manakov problem of the soliton theory. Finally, we apply the later numerical inverse scattering results for constructing related numerical solutions for equations of the Novikov-Veselov hierarchy at fixed positive energy . |
