Acoustic Scattering and the Extended Korteweg deVries hierarchy
solv-int
2007-05-23 v1 Exactly Solvable and Integrable Systems
Abstract
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.
Cite
@article{arxiv.solv-int/9901007,
title = {Acoustic Scattering and the Extended Korteweg deVries hierarchy},
author = {R. Beals and D. H. Sattinger and J. Szmigielski},
journal= {arXiv preprint arXiv:solv-int/9901007},
year = {2007}
}
Comments
18 pages