INVERSE SCATTERING PROBLEM ON THE HALF-LINE AND POSITON SOLUTIONS OF THE KdV EQUATION

摘要

The inverse scattering problem for the Schroedinger operator on the half-line is studied for potentials of positon type with long range oscillating tails at infinity. The inverse problem can be solved for the scattering matrices with arbitrary finite phase shift. Solution of the inverse problem is unique if the following scattering data are given: scattering matrix, energies of the bound states and the corresponding normalizing constants zeroes of the spectral density on the real line.