Iryna Egorova, Johanna Michor, and Gerald Teschl
Soliton Solutions of the Toda Hierarchy on Quasi-Periodic Background Revisited
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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.