Energy-dependent potentials revisited: a universal hierarchy of hydrodynamic type
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2002
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Elsevier
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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 Schrodinger 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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©2002 Elsevier Science B.V. All rights reserved.
A.B. Shabat was supported by the Russian Foundation for Basic Research (Grant Nos. 96-15-96093 and 98-01- 01161), INTAS (Grant No. 99-1782) and a Rotschild professorship. L. Martı́nez Alonso was supported by the Fundación Banco Bilbao Vizcaya Argentaria. Both authors wish to thank the organizers of the program Integrable Systems at the Newton Institute of Cambridge University for their warm hospitality.