This article is cited 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.

MSC: 53A05; 35A30; 35C05; 37K35

Received: May 7, 2014; in final form August 14, 2014; Published online August 25, 2014

Language: English

DOI: 10.3842/SIGMA.2014.091

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ArXiv: 1111.2027