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Acoustic Scattering and the Extended Korteweg deVries hierarchy

R. Beals·D. H. Sattinger·J. Szmigielski
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Abstract

The acoustic scattering operator on the real line is mapped to a Schrödinger operator under the Liouville transformation. The potentials in the image are characterized precisely in terms of their scattering data, and the inverse transformation is obtained as a simple, linear quadrature. An existence theorem for the associated Harry Dym flows is proved, using the scattering method. The scattering problem associated with the Camassa-Holm flows on the real line is solved explicitly for a special case, which is used to reduce a general class of such problems to scattering problems on finite intervals.

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R. Beals, D. H. Sattinger, J. Szmigielski. 1999-01-21. Acoustic Scattering and the Extended Korteweg deVries hierarchy. https://arxiv.org/abs/solv-int/9901007

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