On Stieltjes relations, Painlev\'e-IV hierarchy and complex monodromy
Veselov, A. P.
arXiv, 0012040 / Harvested from arXiv
Text on arXiv
A generalisation of the Stieltjes relations for the Painlev\'e-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 Painlev\'e-IV equation. The approach is based on the interpretation of the Stieltjes relations as local trivial monodromy conditions for certain Schr\"odinger equations in the complex domain. As a corollary a new class of the Schr\"odinger operators with trivial monodromy is constructed in terms of the Painlev\'e-IV transcendents.
Publié le : 2000-12-22
Classification:  Mathematical Physics,  Mathematics - Complex Variables,  33E17, 34M55 
@article{0012040,
     author = {Veselov, A. P.},
     title = {On Stieltjes relations, Painlev\'e-IV hierarchy and complex monodromy},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0012040}
}

Veselov, A. P. On Stieltjes relations, Painlev\'e-IV hierarchy and complex monodromy. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0012040/