Flat structure and potential vector fields related with algebraic solutions to Painlevé VI equation

Flat structure and potential vector fields related with algebraic solutions to Painlevé VI equation

A potential vector field is a solution of an extended WDVV equation which is a generalization of a WDVV equation. It is expected that potential vector fields corresponding to algebraic solutions of Painlevé VI equation can be written by using polynomials or algebraic functions explicitly. The purpo...

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Main Authors: Mitsuo Kato, Toshiyuki Mano, Jiro Sekiguchi
Format: Article
Language:English
Published: AGH Univeristy of Science and Technology Press 2018-01-01
Series:Opuscula Mathematica
Subjects:
flat structure
Painlevé VI equation
algebraic solution
potential vector field
Online Access:http://www.opuscula.agh.edu.pl/vol38/2/art/opuscula_math_3810.pdf
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spelling doaj-2ef0db6befe642c88d86033ac367b7d12020-11-24T23:46:52ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742018-01-01382201252https://doi.org/10.7494/OpMath.2018.38.2.2013810Flat structure and potential vector fields related with algebraic solutions to Painlevé VI equationMitsuo Kato0Toshiyuki Mano1Jiro Sekiguchi2University of the Ryukyus, Colledge of Educations, Department of Mathematics, Nishihara-cho, Okinawa 903-0213, JapanUniversity of the Ryukyus, Faculty of Science, Department of Mathematical Sciences, Nishihara-cho, Okinawa 903-0213, JapanTokyo University of Agriculture and Technology, Faculty of Engineering, Department of Mathematics, Koganei, Tokyo 184-8588, JapanA potential vector field is a solution of an extended WDVV equation which is a generalization of a WDVV equation. It is expected that potential vector fields corresponding to algebraic solutions of Painlevé VI equation can be written by using polynomials or algebraic functions explicitly. The purpose of this paper is to construct potential vector fields corresponding to more than thirty non-equivalent algebraic solutions.http://www.opuscula.agh.edu.pl/vol38/2/art/opuscula_math_3810.pdfflat structurePainlevé VI equationalgebraic solutionpotential vector field
collection DOAJ
language English
format Article
sources DOAJ
author Mitsuo Kato
Toshiyuki Mano
Jiro Sekiguchi
spellingShingle Mitsuo Kato
Toshiyuki Mano
Jiro Sekiguchi
Flat structure and potential vector fields related with algebraic solutions to Painlevé VI equation
Opuscula Mathematica
flat structure
Painlevé VI equation
algebraic solution
potential vector field
author_facet Mitsuo Kato
Toshiyuki Mano
Jiro Sekiguchi
author_sort Mitsuo Kato
title Flat structure and potential vector fields related with algebraic solutions to Painlevé VI equation
title_short Flat structure and potential vector fields related with algebraic solutions to Painlevé VI equation
title_full Flat structure and potential vector fields related with algebraic solutions to Painlevé VI equation
title_fullStr Flat structure and potential vector fields related with algebraic solutions to Painlevé VI equation
title_full_unstemmed Flat structure and potential vector fields related with algebraic solutions to Painlevé VI equation
title_sort flat structure and potential vector fields related with algebraic solutions to painlevé vi equation
publisher AGH Univeristy of Science and Technology Press
series Opuscula Mathematica
issn 1232-9274
publishDate 2018-01-01
description A potential vector field is a solution of an extended WDVV equation which is a generalization of a WDVV equation. It is expected that potential vector fields corresponding to algebraic solutions of Painlevé VI equation can be written by using polynomials or algebraic functions explicitly. The purpose of this paper is to construct potential vector fields corresponding to more than thirty non-equivalent algebraic solutions.
topic flat structure
Painlevé VI equation
algebraic solution
potential vector field
url http://www.opuscula.agh.edu.pl/vol38/2/art/opuscula_math_3810.pdf
work_keys_str_mv AT mitsuokato flatstructureandpotentialvectorfieldsrelatedwithalgebraicsolutionstopainleveviequation
AT toshiyukimano flatstructureandpotentialvectorfieldsrelatedwithalgebraicsolutionstopainleveviequation
AT jirosekiguchi flatstructureandpotentialvectorfieldsrelatedwithalgebraicsolutionstopainleveviequation
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