A Reciprocal Transformation for the Constant Astigmatism Equation

作者：Hlavac Adam^*; Marvan Michal

来源：Symmetry Integrability and Geometry-Methods and Applications, 2014, 10: 091.

DOI：10.3842/SIGMA.2014.091

• constant astigmatism equation
• exact solution
• constant astigmatism surface
• orthogonal equiareal pattern
• reciprocal transformation
• sine-Gordon equation

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 Backlund transformation of the sine-Gordon equation with the Backlund parameter lambda = +/- 1. It is also a nonlocal symmetry.

• 出版日期2014