On Lipschitz solutions of the constant astigmatism equation

JOURNAL OF GEOMETRY AND PHYSICS

卷:85

Article

Hlavac, Adam¹  Marvan, Michal¹ 

[1] Silesian Univ Opava, Math Inst Opava, Opava 74601, Czech Republic

关键词: Constant astigmatism equation;    Constant astigmatism surface;    Orthogonal equiareal pattern;    sine-Gordon equation;    Symmetry invariant solution;    Slip-line field;   

DOI  :  10.1016/j.geomphys.2014.05.020

来源: Elsevier

【 摘 要 】

We show that the solutions of the constant astigmatism equation that correspond to a class of surfaces found by Lipschitz in 1887, exactly match the Lie symmetry invariant solutions and constitute a four-dimensional manifold. The two-dimensional orbit space with respect to the Lie symmetry group is described. Our approach relies on the link between constant astigmatism surfaces and orthogonal equiareal patterns. The counterpart sine-Gordon solutions are shown to be Lie symmetry invariant as well. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free