A Reciprocal Transformation for the Constant Astigmatism Equation

Symmetry Integrability and Geometry-Methods and Applications

article

Adam HlaváčMichal Marvan¹ 

[1] Mathematical Institute in Opava, Silesian University in Opava

关键词: constant astigmatism equation;    exact solution;    constant astigmatism surface;    orthogonal equiareal pattern;    reciprocal transformation;    sine-Gordon equation;   

DOI  :  10.3842/SIGMA.2014.091

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown