WebAug 17, 2014 · Title: Geometric Analysis of Reductions from Schlesinger Transformations to Difference Painlevé Equations. ... Mathematical Physics (math-ph); Algebraic Geometry (math.AG); Classical Analysis and ODEs (math.CA); Exactly Solvable and Integrable Systems (nlin.SI) MSC classes: 34M55, 34M56, 14E07: Cite as: …
[1408.3778] Geometric Analysis of Reductions from …
WebThis in turn leads to a 2g-parameter family of solutions of the corresponding Schlesinger equations, explicitly described in terms of Riemann theta functions of genus g. In the case g = 1 the solution found coincides with the general elliptic solution of the particular case of the Painlevé VI equation first obtained by N. J. Hitchin [H1]. WebJan 12, 2024 · The study of geometric aspects of the Painlevé equations, which is a main topic of this paper, has been initiated by Okamoto's pioneering work . ... We note that is … shoe cover size chart
Painlevé Equations and Related Topics : Proceedings of the ...
WebJun 20, 2015 · A new method to construct algebro-geometric solutions of rank two Schlesinger systems is presented. For an elliptic curve represented as a ramified double covering of CP^1, a meromorphic differential is constructed with the following property: the common projection of its two zeros on the base of the covering, regarded as a function of … WebFeb 28, 2024 · Abstract. A new form of algebro-geometric solutions of Rank 2 Schlesinger systems is presented. The solutions are written in terms of a particular meromorphic differential of the third type on hyperelliptic curves represented as a ramified double coverings of ℂ ℙ 1 .As was shown in the authors' earlier paper, in the case of genus one, … WebSep 28, 2015 · In this paper a comprehensive review is given on the current status of achievements in the geometric aspects of the Painlevé equations, with a particular emphasis on the discrete Painlevé equations. The theory is controlled by the geometry of certain rational surfaces called the spaces of initial values, which are characterized by … shoe covers menards