pseudospherical surface


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pseudospherical surface

[‚süd·ō¦sfer·ə·kəl ′sər·fəs]
(mathematics)
A surface whose total curvature has a constant negative value.
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Elliptic Sinh-Gordon Equation Derived from Pseudospherical Surfaces. In this section, we will derive elliptic sinhGordon equation from pseudospherical surfaces.
In this paper, we obtain sinh-Gordon equation and elliptic sinh-Gordon equation by means of pseudospherical surfaces. In addition, we give the Baacklund transformations and nonlinear superposition formulas of sinh-Gordon equation and elliptic sinh-Gordon equation, which lead to new exact solutions of the sinh-Gordon equation and elliptic sinh-Gordon equation.