Iryna Egorova, Johanna Michor, and Gerald Teschl
Soliton Solutions of the Toda Hierarchy on Quasi-Periodic Background Revisited
(49K, LaTeX)

ABSTRACT.  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.