On Differential Equations Derived from the Pseudospherical Surfaces
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 σ = −2, σ = −1, respectively. By employing the Bäcklund transforma...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/381717 |
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| _version_ | 1832567226731855872 |
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| author | Hongwei Yang Xiangrong Wang Baoshu Yin |
| author_facet | Hongwei Yang Xiangrong Wang Baoshu Yin |
| author_sort | Hongwei Yang |
| collection | DOAJ |
| description | 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 σ = −2, σ = −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. |
| format | Article |
| id | doaj-art-411ab78aa85c4b22b651734d2adb514a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-411ab78aa85c4b22b651734d2adb514a2025-02-03T01:01:58ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/381717381717On Differential Equations Derived from the Pseudospherical SurfacesHongwei Yang0Xiangrong Wang1Baoshu Yin2College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaInstitute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, ChinaWe 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 σ = −2, σ = −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.http://dx.doi.org/10.1155/2014/381717 |
| spellingShingle | Hongwei Yang Xiangrong Wang Baoshu Yin On Differential Equations Derived from the Pseudospherical Surfaces Abstract and Applied Analysis |
| title | On Differential Equations Derived from the Pseudospherical Surfaces |
| title_full | On Differential Equations Derived from the Pseudospherical Surfaces |
| title_fullStr | On Differential Equations Derived from the Pseudospherical Surfaces |
| title_full_unstemmed | On Differential Equations Derived from the Pseudospherical Surfaces |
| title_short | On Differential Equations Derived from the Pseudospherical Surfaces |
| title_sort | on differential equations derived from the pseudospherical surfaces |
| url | http://dx.doi.org/10.1155/2014/381717 |
| work_keys_str_mv | AT hongweiyang ondifferentialequationsderivedfromthepseudosphericalsurfaces AT xiangrongwang ondifferentialequationsderivedfromthepseudosphericalsurfaces AT baoshuyin ondifferentialequationsderivedfromthepseudosphericalsurfaces |