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Old and new doubly periodic solutions of the Sinh-Gordon equation. (English) Zbl 0635.35029

New results in nonlinear partial differential equations, Semin. Bonn/FRG 1984, Aspects. Math. E10, 37-73 (1987).
[For the entire collection see Zbl 0606.00011.]
The author investigates existence of doubly periodic solutions to the equation \(u_{xx}+u_{yy}+\sinh 2u=0\) in connection with a similar problem for a corresponding system of 10 integrable equations of the first order. The results gained are used to the construction of immersed constant mean curvature surfaces in \(R^ 3\).
Reviewer: O.Vejvoda

MSC:

35J60 Nonlinear elliptic equations
35B10 Periodic solutions to PDEs
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature

Citations:

Zbl 0606.00011