On differential equations derived from the pseudospherical surfaces (Q1723976)
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scientific article; zbMATH DE number 7022270
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On differential equations derived from the pseudospherical surfaces |
scientific article; zbMATH DE number 7022270 |
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On differential equations derived from the pseudospherical surfaces (English)
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14 February 2019
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Summary: We construct two metric tensor fields; by means of these metric tensor fields, sinh-Gordon equation and elliptic sinh-Gordon equation are obtained, which describe pseudospherical surfaces of constant negative Riemann curvature scalar \(\sigma\) = \(-\)2, \(\sigma\) = \(-\)1, respectively. By employing the Bäcklund transformation, nonlinear superposition formulas of sinh-Gordon equation and elliptic sinh-Gordon equation are derived; various new exact solutions of the equations are obtained.
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sinh-Gordon equation
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elliptic sinh-Gordon equation
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Bäcklund transformation
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tensor fields
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0.97988427
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