1201.5768 (Iryna Egorova et al.)

Scattering theory with finite-gap backgrounds: Transformation operators
and characteristic properties of scattering data    [PDF]

Iryna Egorova, Johanna Michor, Gerald Teschl

We develop direct and inverse scattering theory for Jacobi operators with
steplike coefficients which are asymptotically close to different finite-gap
quasi-periodic coefficients on different sides. We give a complete
characterization of the scattering data, which allows unique solvability of the
inverse scattering problem for perturbations with finite second moment.

View original: http://arxiv.org/abs/1201.5768