Non-Classical Symmetry Analysis of a Class of Nonlinear Lattice Equations
In this paper, a non-classical symmetry method for obtaining the symmetries of differential–difference equations is proposed. The non-classical symmetry method introduces an additional constraint known as the invariant surface condition, which is applied after the infinitesimal transformation. By so...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-12-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/12/2199 |
| _version_ | 1797379296708263936 |
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| author | Wenting Li Yueting Chen Kun Jiang |
| author_facet | Wenting Li Yueting Chen Kun Jiang |
| author_sort | Wenting Li |
| collection | DOAJ |
| description | In this paper, a non-classical symmetry method for obtaining the symmetries of differential–difference equations is proposed. The non-classical symmetry method introduces an additional constraint known as the invariant surface condition, which is applied after the infinitesimal transformation. By solving the governing equations that satisfy this condition, we can obtain the corresponding reduced equation. This allows us to determine the non-classical symmetry of the differential–difference equation. This method avoids the complicated calculation involved in extending the infinitesimal generator and allows for a wider range of symmetry forms. As a result, it enables the derivation of a greater number of differential–difference equations. In this paper, two kinds of (2+1)-dimensional Toda-like lattice equations are taken as examples, and their corresponding symmetric and reduced equations are obtained using the non-classical symmetry method. |
| first_indexed | 2024-03-08T20:20:06Z |
| format | Article |
| id | doaj.art-7ccc5bd9748d46b4b979f6e37c7c0187 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-08T20:20:06Z |
| publishDate | 2023-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-7ccc5bd9748d46b4b979f6e37c7c01872023-12-22T14:45:23ZengMDPI AGSymmetry2073-89942023-12-011512219910.3390/sym15122199Non-Classical Symmetry Analysis of a Class of Nonlinear Lattice EquationsWenting Li0Yueting Chen1Kun Jiang2Faculty of Teacher Education, Qiongtai Normal University, Haikou 571127, ChinaFaculty of Teacher Education, Qiongtai Normal University, Haikou 571127, ChinaSchool of Educational Sciences, Harbin Normal University, Harbin 150080, ChinaIn this paper, a non-classical symmetry method for obtaining the symmetries of differential–difference equations is proposed. The non-classical symmetry method introduces an additional constraint known as the invariant surface condition, which is applied after the infinitesimal transformation. By solving the governing equations that satisfy this condition, we can obtain the corresponding reduced equation. This allows us to determine the non-classical symmetry of the differential–difference equation. This method avoids the complicated calculation involved in extending the infinitesimal generator and allows for a wider range of symmetry forms. As a result, it enables the derivation of a greater number of differential–difference equations. In this paper, two kinds of (2+1)-dimensional Toda-like lattice equations are taken as examples, and their corresponding symmetric and reduced equations are obtained using the non-classical symmetry method.https://www.mdpi.com/2073-8994/15/12/2199non-classical symmetryLattice equationLie symmetrydifferential–difference equation |
| spellingShingle | Wenting Li Yueting Chen Kun Jiang Non-Classical Symmetry Analysis of a Class of Nonlinear Lattice Equations Symmetry non-classical symmetry Lattice equation Lie symmetry differential–difference equation |
| title | Non-Classical Symmetry Analysis of a Class of Nonlinear Lattice Equations |
| title_full | Non-Classical Symmetry Analysis of a Class of Nonlinear Lattice Equations |
| title_fullStr | Non-Classical Symmetry Analysis of a Class of Nonlinear Lattice Equations |
| title_full_unstemmed | Non-Classical Symmetry Analysis of a Class of Nonlinear Lattice Equations |
| title_short | Non-Classical Symmetry Analysis of a Class of Nonlinear Lattice Equations |
| title_sort | non classical symmetry analysis of a class of nonlinear lattice equations |
| topic | non-classical symmetry Lattice equation Lie symmetry differential–difference equation |
| url | https://www.mdpi.com/2073-8994/15/12/2199 |
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