A Reciprocal Transformation for the Constant Astigmatism Equation 3 2 Point symmetries

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. 

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