Geodesic
A Reciprocal Transformation for the Constant Astigmatism Equation
Symmetry, integrability and geometry: methods and applications, Tome 10 (2014) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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Adam Hlaváč; Michal Marvan. A Reciprocal Transformation for the Constant Astigmatism Equation. Symmetry, integrability and geometry: methods and applications, Tome 10 (2014). http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a90/

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