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On Stieltjes relations, Painlevé-IV hierarchy and complex monodromy

A. P. Veselov
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Abstract

A generalisation of the Stieltjes relations for the Painlevé-IV transcendents and their higher analogues determined by the dressing chains is proposed. It is proven that if a rational function from a certain class satisfies these relations it must be a solution of some higher Painlevé-IV equation. The approach is based on the interpretation of the Stieltjes relations as local trivial monodromy conditions for certain Schrödinger equations in the complex domain. As a corollary a new class of the Schrödinger operators with trivial monodromy is constructed in terms of the Painlevé-IV transcendents.

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A. P. Veselov. 2000-12-22. On Stieltjes relations, Painlevé-IV hierarchy and complex monodromy. https://doi.org/10.1088/0305-4470%2F34%2F16%2F318

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