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Reciprocal transformations, Painlevé property and solutions of energy-dependent Schrödinger hierarchies. (English) Zbl 1044.37531
Summary: Energy-dependent Schrödinger hierarchies of KdV type provide examples of systems with the weak Painlevé property. We propose reciprocal transformations such that the transformed systems satisfy the standard (strong) Painlevé test of Weiss, Tabor and Carnevale (WTC). The reciprocal transformations are used to derive some exact solutions.

MSC:
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35Q53 KdV equations (Korteweg-de Vries equations)
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