Math. Nachr. 282:4, 526-539 (2009) [DOI: 10.1002/mana.200610752]
Soliton Solutions of the Toda Hierarchy on Quasi-Periodic Backgrounds Revisited
Iryna Egorova, Johanna Michor, and Gerald Teschl
We investigate soliton solutions of the Toda hierarchy on a quasi-periodic finite-gap background by means of the double commutation method and the inverse scattering transform. In particular, we compute the phase shift caused by a soliton on a quasi-periodic finite-gap background. Furthermore, we consider short-range perturbations via scattering theory. We give a full description of the effect of the double commutation method on the scattering data and establish the inverse scattering transform in this setting.