Energy-dependent potentials revisited: A universal hierarchy of hydrodynamic type
Exactly Solvable and Integrable Systems
2015-06-26 v1
Abstract
A hierarchy of infinite-dimensional systems of hydrodynamic type is considered and a general scheme for classifying its reductions is provided. Wide families of integrable systems including, in particular, those associated with energy-dependent spectral problems of Schr\" odinger type, are characterized as reductions of this hierarchy. -phase type reductions and their corresponding Dubrovin equations are analyzed. A symmetry transformation connecting different classes of reductions is formulated.
Cite
@article{arxiv.nlin/0202008,
title = {Energy-dependent potentials revisited: A universal hierarchy of hydrodynamic type},
author = {L. Martinez Alonso and A. B. Shabat},
journal= {arXiv preprint arXiv:nlin/0202008},
year = {2015}
}
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LaTex 16 pages