New Explicit Solutions of the Extended Double (2+1)-Dimensional Sine-Gorden Equation and Its Time Fractional Form
In this paper, the extended double (2+1)-dimensional sine-Gorden equation is studied. First of all, using the symmetry method, the corresponding vector fields, Lie algebra and infinitesimal generators are derived. Then, from infinitesimal generators, the symmetry reductions are presented. In additio...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/3/166 |
| _version_ | 1797471483623112704 |
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| author | Gangwei Wang Li Li Qi Wang Juan Geng |
| author_facet | Gangwei Wang Li Li Qi Wang Juan Geng |
| author_sort | Gangwei Wang |
| collection | DOAJ |
| description | In this paper, the extended double (2+1)-dimensional sine-Gorden equation is studied. First of all, using the symmetry method, the corresponding vector fields, Lie algebra and infinitesimal generators are derived. Then, from infinitesimal generators, the symmetry reductions are presented. In addition, these reduced equations are converted into the corresponding partial differential equations, which including classical double (1+1)-dimensional sine-Gorden equation. Moreover, based on the Lie symmetry method again, these reduced equations are investigated. Meanwhile, based on traveling wave transformation, some explicit solutions of the extended double (2+1)-dimensional sine-Gorden equation are obtained. Consequently, a conservation law is derived via conservation law multiplier method. Finally, especially with the help of the fractional complex transform, some solutions of double time fractional (2+1)-dimensional sine-Gorden equation are also derived. These results might explain complex nonlinear phenomenon. |
| first_indexed | 2024-03-09T19:48:59Z |
| format | Article |
| id | doaj.art-231073ec28a64f758736efb1c82849f8 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T19:48:59Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-231073ec28a64f758736efb1c82849f82023-11-24T01:14:46ZengMDPI AGFractal and Fractional2504-31102022-03-016316610.3390/fractalfract6030166New Explicit Solutions of the Extended Double (2+1)-Dimensional Sine-Gorden Equation and Its Time Fractional FormGangwei Wang0Li Li1Qi Wang2Juan Geng3School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, ChinaLibrary of Hebei University of Economics and Business, Shijiazhuang 050061, ChinaSchool of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, ChinaSchool of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, ChinaIn this paper, the extended double (2+1)-dimensional sine-Gorden equation is studied. First of all, using the symmetry method, the corresponding vector fields, Lie algebra and infinitesimal generators are derived. Then, from infinitesimal generators, the symmetry reductions are presented. In addition, these reduced equations are converted into the corresponding partial differential equations, which including classical double (1+1)-dimensional sine-Gorden equation. Moreover, based on the Lie symmetry method again, these reduced equations are investigated. Meanwhile, based on traveling wave transformation, some explicit solutions of the extended double (2+1)-dimensional sine-Gorden equation are obtained. Consequently, a conservation law is derived via conservation law multiplier method. Finally, especially with the help of the fractional complex transform, some solutions of double time fractional (2+1)-dimensional sine-Gorden equation are also derived. These results might explain complex nonlinear phenomenon.https://www.mdpi.com/2504-3110/6/3/166extended double (2+1)-dimensional sine-Gorden equationtime fractional formLie symmetrysymmetry reductionsexplicit solutionsconservation laws |
| spellingShingle | Gangwei Wang Li Li Qi Wang Juan Geng New Explicit Solutions of the Extended Double (2+1)-Dimensional Sine-Gorden Equation and Its Time Fractional Form Fractal and Fractional extended double (2+1)-dimensional sine-Gorden equation time fractional form Lie symmetry symmetry reductions explicit solutions conservation laws |
| title | New Explicit Solutions of the Extended Double (2+1)-Dimensional Sine-Gorden Equation and Its Time Fractional Form |
| title_full | New Explicit Solutions of the Extended Double (2+1)-Dimensional Sine-Gorden Equation and Its Time Fractional Form |
| title_fullStr | New Explicit Solutions of the Extended Double (2+1)-Dimensional Sine-Gorden Equation and Its Time Fractional Form |
| title_full_unstemmed | New Explicit Solutions of the Extended Double (2+1)-Dimensional Sine-Gorden Equation and Its Time Fractional Form |
| title_short | New Explicit Solutions of the Extended Double (2+1)-Dimensional Sine-Gorden Equation and Its Time Fractional Form |
| title_sort | new explicit solutions of the extended double 2 1 dimensional sine gorden equation and its time fractional form |
| topic | extended double (2+1)-dimensional sine-Gorden equation time fractional form Lie symmetry symmetry reductions explicit solutions conservation laws |
| url | https://www.mdpi.com/2504-3110/6/3/166 |
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