English

A Reciprocal Transformation for the Constant Astigmatism Equation

Exactly Solvable and Integrable Systems 2014-08-28 v3 Differential Geometry

Abstract

We introduce a nonlocal transformation to generate exact solutions of the constant astigmatism equation zyy+(1/z)xx+2=0z_{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 λ=±1\lambda = \pm1. It is also a nonlocal symmetry.

Keywords

Cite

@article{arxiv.1111.2027,
  title  = {A Reciprocal Transformation for the Constant Astigmatism Equation},
  author = {Adam Hlaváč and Michal Marvan},
  journal= {arXiv preprint arXiv:1111.2027},
  year   = {2014}
}
R2 v1 2026-06-21T19:33:00.070Z