Symmetries for the Semi-Discrete Lattice Potential Korteweg–de Vries Equation
In this paper, we prove that the isospectral flows associated with both the <i>x</i>-part and the <i>n</i>-part of the Lax pair of the semi-discrete lattice potential Korteweg–de Vries equation are symmetries of the equation. Furthermore, we show that these two hierarchies of...
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MDPI AG
2024-12-01
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| author | Junwei Cheng Xiang Tian |
| author_facet | Junwei Cheng Xiang Tian |
| author_sort | Junwei Cheng |
| collection | DOAJ |
| description | In this paper, we prove that the isospectral flows associated with both the <i>x</i>-part and the <i>n</i>-part of the Lax pair of the semi-discrete lattice potential Korteweg–de Vries equation are symmetries of the equation. Furthermore, we show that these two hierarchies of symmetries are equivalent. Additionally, we construct the non-isospectral flows associated with the <i>x</i>-part of the Lax pair, which can be interpreted as the master symmetries of the semi-discrete lattice potential Korteweg–de Vries equation. |
| format | Article |
| id | doaj-art-03037003b2ca401588029d6faf5563c1 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj-art-03037003b2ca401588029d6faf5563c12025-01-10T13:18:18ZengMDPI AGMathematics2227-73902024-12-0113111710.3390/math13010117Symmetries for the Semi-Discrete Lattice Potential Korteweg–de Vries EquationJunwei Cheng0Xiang Tian1School of Information Science and Engineering, Shandong Agricultural University, Taian 271018, ChinaSchool of Information Science and Engineering, Shandong Agricultural University, Taian 271018, ChinaIn this paper, we prove that the isospectral flows associated with both the <i>x</i>-part and the <i>n</i>-part of the Lax pair of the semi-discrete lattice potential Korteweg–de Vries equation are symmetries of the equation. Furthermore, we show that these two hierarchies of symmetries are equivalent. Additionally, we construct the non-isospectral flows associated with the <i>x</i>-part of the Lax pair, which can be interpreted as the master symmetries of the semi-discrete lattice potential Korteweg–de Vries equation.https://www.mdpi.com/2227-7390/13/1/117semi-discrete lattice potential KdV equationsymmetriesLax pairzero-curvature representation |
| spellingShingle | Junwei Cheng Xiang Tian Symmetries for the Semi-Discrete Lattice Potential Korteweg–de Vries Equation Mathematics semi-discrete lattice potential KdV equation symmetries Lax pair zero-curvature representation |
| title | Symmetries for the Semi-Discrete Lattice Potential Korteweg–de Vries Equation |
| title_full | Symmetries for the Semi-Discrete Lattice Potential Korteweg–de Vries Equation |
| title_fullStr | Symmetries for the Semi-Discrete Lattice Potential Korteweg–de Vries Equation |
| title_full_unstemmed | Symmetries for the Semi-Discrete Lattice Potential Korteweg–de Vries Equation |
| title_short | Symmetries for the Semi-Discrete Lattice Potential Korteweg–de Vries Equation |
| title_sort | symmetries for the semi discrete lattice potential korteweg de vries equation |
| topic | semi-discrete lattice potential KdV equation symmetries Lax pair zero-curvature representation |
| url | https://www.mdpi.com/2227-7390/13/1/117 |
| work_keys_str_mv | AT junweicheng symmetriesforthesemidiscretelatticepotentialkortewegdevriesequation AT xiangtian symmetriesforthesemidiscretelatticepotentialkortewegdevriesequation |