Inverse scattering transformation for positons

The scattering problem for the one-dimensional Schrodinger operator with po tential equal to the positon solution of the Korteweg-de Vries (KdV) equati on is investigated. It is shown that the transition coefficient is equal to zero and different positon potentials can have the same reflection coeffic ient, i.e. the inverse scattering problem cannot be solved uniquely. It is observed that the reflection coefficient calculated for the positon solutio ns does not change with time in accordance with the inverse scattering meth od for KdV.