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Symmetry, Integrability and Geometry: Methods and Applications, 2011, Volume 7, 049, 13 pp.
DOI: https://doi.org/10.3842/SIGMA.2011.049
(Mi sigma607)
 

This article is cited in 1 scientific paper (total in 1 paper)

Symmetries in Connection Preserving Deformations

Christopher M. Ormerod

La Trobe University, Department of Mathematics and Statistics, Bundoora VIC 3086, Australia
Full-text PDF (354 kB) Citations (1)
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Abstract: We wish to show that the root lattice of Bäcklund transformations of the $q$-analogue of the third and fourth Painlevé equations, which is of type $(A_2+A_1)^{(1)}$, may be expressed as a quotient of the lattice of connection preserving deformations. Furthermore, we will show various directions in the lattice of connection preserving deformations present equivalent evolution equations under suitable transformations. These transformations correspond to the Dynkin diagram automorphisms.
Keywords: $q$-Painlevé; Lax pairs; $q$-Schlesinger transformations; connection; isomonodromy.
Received: January 31, 2011; in final form May 18, 2011; Published online May 24, 2011
Bibliographic databases:
Document Type: Article
MSC: 34M55; 39A13
Language: English
Citation: Christopher M. Ormerod, “Symmetries in Connection Preserving Deformations”, SIGMA, 7 (2011), 049, 13 pp.
Citation in format AMSBIB
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\paper Symmetries in Connection Preserving Deformations
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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