A Reciprocal Transformation for the Constant Astigmatism Equation

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 Bäcklund transformation of the sine-Gordon equation with the Bäcklund parameter $\lambda =\pm 1$. It is also a nonlocal symmetry.

References in corpus (4)

• Exact Solutions to the Sine-Gordon Equation
• On integrability of Weingarten surfaces: a forgotten class
• The Constant Astigmatism Equation. New Exact Solution
• Classification of integrable Weingarten surfaces possessing an sl(2)-valued zero curvature representation

Cited by in corpus (4)

• The Constant Astigmatism Equation. New Exact Solution
• On multisoliton solutions of the constant astigmatism equation
• More exact solutions of the constant astigmatism equation
• Nonlocal conservation laws of the constant astigmatism equation