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Energy-dependent potentials revisited: A universal hierarchy of hydrodynamic type

L. Martinez Alonso·A. B. Shabat
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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. $N$-phase type reductions and their corresponding Dubrovin equations are analyzed. A symmetry transformation connecting different classes of reductions is formulated.

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L. Martinez Alonso, A. B. Shabat. 2002-02-04. Energy-dependent potentials revisited: A universal hierarchy of hydrodynamic type. https://doi.org/10.1016/s0375-9601(02)00662-x

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