A Reciprocal Transformation for the Constant Astigmatism Equation

Published 8 Nov 2011 in nlin.SI and math.DG | (1111.2027v3)

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 B\"acklund transformation of the sine-Gordon equation with the B\"acklund parameter $\lambda = \pm1$. It is also a nonlocal symmetry.

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