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Symmetry, Integrability and Geometry: Methods and Applications, 2023, Volume 19, 094, 17 pp.
DOI: https://doi.org/10.3842/SIGMA.2023.094 (Mi sigma1989) 		 
A $3 \times 3$ Lax Form for the $q$-Painlevé Equation of Type $E_6$

Kanam Park

National Institute of Technology, Toba College, 1-1, Ikegami-cho, Toba-shi, Mie, Japan
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DOI: https://doi.org/10.3842/SIGMA.2023.094
Abstract: For the $q$-Painlevé equation with affine Weyl group symmetry of type $E_6^{(1)}$, a $2\times 2$ matrix Lax form and a second order scalar lax form were known. We give a new $3\times 3$ matrix Lax form and a third order scalar equation related to it. Continuous limit is also discussed.
Keywords: Lax formalism, $q$-Painlevé equation.
Funding agency Grant number
Japan Society for the Promotion of Science 17H06127
Japan Science and Technology Agency 26287018
She also thanks supports from JSPS KAKENHI Grant Numbers 17H06127 and 26287018 for the travel expenses in accomplishing this study.
Received: December 1, 2022; in final form November 5, 2023; Published online November 18, 2023
Document Type: Article
MSC: 14H70, 34M56, 39A13
Language: English
Citation: Kanam Park, “A $3 \times 3$ Lax Form for the $q$-Painlevé Equation of Type $E_6$”, SIGMA, 19 (2023), 094, 17 pp.
Citation in format AMSBIB
\Bibitem{Par23}
\by Kanam~Park
\paper A $3 \times 3$ Lax Form for the $q$-Painlev\'e Equation of Type $E_6$
\jour SIGMA
\yr 2023
\vol 19
\papernumber 094
\totalpages 17
\mathnet{http://mi.mathnet.ru/sigma1989}
\crossref{https://doi.org/10.3842/SIGMA.2023.094}
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