Abstract
AbstractWe 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 (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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