Article

**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.

** MSC2000:** Primary 37K15, 37K10; Secondary 47B36, 34L25

**Keywords:** *Solitons, Toda hierarchy, periodic, inverse scattering transform*

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