Acoustic Scattering and the Extended Korteweg deVries hierarchy

Details Acoustic Scattering and the Extended Korteweg deVries hierarchy Acoustic Scattering and the Extended Korteweg deVries hierarchy

1999-01-21

arxiv.org/abs/solv-int/9901007v1

Advances in Mathematics, vol 140, (1998), 190-206

Nonlinear Sciences

Exactly Solvable and Integrable Systems

18 pages

Scientific paper

The acoustic scattering operator on the real line is mapped to a Schr\"odinger 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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