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Soliton Solutions of the Toda Hierarchy on Quasi-Periodic Backgrounds Revisited

Iryna Egorova·Johanna Michor·Gerald Teschl
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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.

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Iryna Egorova, Johanna Michor, Gerald Teschl. 2007-03-26. Soliton Solutions of the Toda Hierarchy on Quasi-Periodic Backgrounds Revisited. https://doi.org/10.1002/mana.200610752

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