Symmetries for the Semi-Discrete Lattice Potential Korteweg–de Vries Equation

Junwei Cheng () and Xiang Tian
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Junwei Cheng: School of Information Science and Engineering, Shandong Agricultural University, Taian 271018, China
Xiang Tian: School of Information Science and Engineering, Shandong Agricultural University, Taian 271018, China

Mathematics, 2024, vol. 13, issue 1, 1-11

Abstract: In this paper, we prove that the isospectral flows associated with both the x -part and the n -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 x -part of the Lax pair, which can be interpreted as the master symmetries of the semi-discrete lattice potential Korteweg–de Vries equation.

Keywords: semi-discrete lattice potential KdV equation; symmetries; Lax pair; zero-curvature representation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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