Zh. Mat. Fiz. Anal. Geom. 4-1, 33-62 (2008) [url]
Scattering Theory for Jacobi Operators with General Steplike Quasi-Periodic Background
Iryna Egorova, Johanna Michor, and 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 allow unique solvability of the inverse scattering problem in the class of perturbations with finite first moment.