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Symmetry, Integrability and Geometry: Methods and Applications, 2014, Volume 10, 091, 20 pp.
DOI: https://doi.org/10.3842/SIGMA.2014.091 (Mi sigma956) 		 
This article is cited in 5 scientific papers (total in 5 papers)

A Reciprocal Transformation for the Constant Astigmatism Equation

Adam Hlaváč, Michal Marvan

Mathematical Institute in Opava, Silesian University in Opava, Na Rybníčku 1, 746 01 Opava, Czech Republic
Full-text PDF (832 kB) Citations (5)
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DOI: https://doi.org/10.3842/SIGMA.2014.091
Abstract: We introduce a nonlocal transformation to generate exact solutions of the constant astigmatism equation $z_{yy} + (1/z)_{xx} + 2 = 0$. The transformation is related to the special case of the famous Bäcklund transformation of the sine-Gordon equation with the Bäcklund parameter $\lambda = \pm1$. It is also a nonlocal symmetry.
Keywords: constant astigmatism equation; exact solution; constant astigmatism surface; orthogonal equiareal pattern; reciprocal transformation; sine-Gordon equation.
Received: May 7, 2014; in final form August 14, 2014; Published online August 25, 2014
Bibliographic databases:
Document Type: Article
MSC: 53A05; 35A30; 35C05; 37K35
Language: English
Citation: Adam Hlaváč, Michal Marvan, “A Reciprocal Transformation for the Constant Astigmatism Equation”, SIGMA, 10 (2014), 091, 20 pp.
Citation in format AMSBIB
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\by Adam~Hlav\'a{\v{c}}, Michal~Marvan
\paper A Reciprocal Transformation for the Constant Astigmatism Equation
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\vol 10
\papernumber 091
\totalpages 20
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Symmetry, Integrability and Geometry: Methods and Applications
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