A $3 \times 3$ Lax Form for the $q$-Painlevé Equation of Type $E_6$
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Published:2023-11-18
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ISSN:1815-0659
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Container-title:Symmetry, Integrability and Geometry: Methods and Applications
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language:
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Short-container-title:SIGMA
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.
Publisher
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
Subject
Geometry and Topology,Mathematical Physics,Analysis