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This article is cited in 4 scientific papers (total in 4 papers)
Cauchy matrix scheme for semidiscrete lattice Korteweg–de Vries-type equations
Maebel Mesfuna, Song-Lin Zhaob a Department of Mathematics, Shanghai University, Shanghai, China
b Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, China
Abstract:
Based on a determining equation set and master function, we consider a Cauchy matrix scheme for three semidiscrete lattice Korteweg–de Vries-type equations. The Lax integrability of these equations is discussed. Various types of solutions, including soliton solutions, Jordan-block solutions, and mixed solutions are derived by solving the determining equation set. Specifically, we find $1$-soliton, $2$-soliton, and the simplest Jordan-block solutions for the semidiscrete lattice potential Korteweg–de Vries equation.
Keywords:
semidiscrete lattice Korteweg–de Vries-type equations, Cauchy
matrix approach, Lax integrability, solution.
Received: 08.10.2021 Revised: 05.11.2021
Citation:
Maebel Mesfun, Song-Lin Zhao, “Cauchy matrix scheme for semidiscrete lattice Korteweg–de Vries-type equations”, TMF, 211:1 (2022), 48–64; Theoret. and Math. Phys., 211:1 (2022), 483–497
Linking options:
https://www.mathnet.ru/eng/tmf10179https://doi.org/10.4213/tmf10179 https://www.mathnet.ru/eng/tmf/v211/i1/p48
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Abstract page: | 154 | Full-text PDF : | 27 | References: | 46 | First page: | 6 |
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