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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