A Reciprocal Transformation for the Constant Astigmatism Equation

Abstract

We introduce a nonlocal transformation to generate exact solutions of the constant astigmatism equation zyy+(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 λ=±1. It is also a nonlocal symmetry.