On Stieltjes relations, Painleve-IV hierarchy and complex monodromy
preprintposted on 2006-01-24, 11:08 authored by Alexander VeselovAlexander Veselov
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.
- Mathematical Sciences
NotesThis 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.