DISCRETIZING CONSTANT CURVATURE SURFACES VIA LOOP GROUP FACTORIZATIONS - THE DISCRETE SINE-GORDON AND SINH-GORDON EQUATIONS
Publication Date
1995
Journal or Book Title
JOURNAL OF GEOMETRY AND PHYSICS
Abstract
The sine- and sinh-Gordon equations are the harmonic map equations for maps of the (Lorentz) plane into the 2-sphere. Geometrically they correspond to the integrability equations for surfaces of constant Gauss and constant mean curvature. There is a well-known dressing action of a loop group on the space of harmonic maps. By discretizing the vacuum solutions we obtain via the dressing action completely integrable discretizations (in both variables) of the sine- and sinh-Gordon equations. For the sine-Gordon equation we get Hirota's discretization. Since we work in a geometric context we also obtain discrete models for harmonic maps into the 2-sphere and discrete models of constant Gauss and mean curvature surfaces.
Pages
245-260
Volume
17
Issue
3
Recommended Citation
Pedit, F and WU, HY, "DISCRETIZING CONSTANT CURVATURE SURFACES VIA LOOP GROUP FACTORIZATIONS - THE DISCRETE SINE-GORDON AND SINH-GORDON EQUATIONS" (1995). JOURNAL OF GEOMETRY AND PHYSICS. 769.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/769
Comments
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