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# On Stieltjes relations, Painleve-IV hierarchy and complex monodromy

preprint
posted on 24.01.2006, 11:08
A generalisation of the Stieltjes relations for the Painleve-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 Painleve-IV equation. The approach is based on the interpretation of the Stieltjes relations as local trivial monodromy conditions for certain Schrodinger equations in the complex domain. As a corollary a new class of the Schrodinger operators with trivial monodromy is constructed in terms of the Painleve-IV transcendents.

• Science

## Department

• Mathematical Sciences

146951 bytes

2001

## Notes

This is a pre-print. The definitive version: VESELOV, A.P.,2001. On Stieltjes relations, Painleve-IV hierarchy and complex monodromy. Journal of Physics A - Mathematical and General, 34(16), pp.3511-3519, is available at: http://www.iop.org/EJ/journal/JPhysA.

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