Energy-dependent potentials revisited: a universal hierarchy of hydrodynamic type
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 Schrödinger 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.
Physics Letters A
- Pub Date:
- July 2002
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- LaTex 16 pages