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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
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
Citation:
Adam Hlaváč, Michal Marvan, “A Reciprocal Transformation for the Constant Astigmatism Equation”, SIGMA, 10 (2014), 091, 20 pp.
Linking options:
https://www.mathnet.ru/eng/sigma956 https://www.mathnet.ru/eng/sigma/v10/p91
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Abstract page: | 150 | Full-text PDF : | 42 | References: | 37 |
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