Geodesic
Cauchy matrix scheme for semidiscrete lattice Korteweg--de~Vries-type equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 211 (2022) no. 1, pp. 48-64

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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
Mots-clés : solution. 
@article{TMF_2022_211_1_a3,
     author = {Maebel Mesfun and Song-Lin Zhao},
     title = {Cauchy matrix scheme for semidiscrete lattice {Korteweg--de~Vries-type} equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {48--64},
     publisher = {mathdoc},
     volume = {211},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2022_211_1_a3/}
}
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Maebel Mesfun; Song-Lin Zhao. Cauchy matrix scheme for semidiscrete lattice Korteweg--de~Vries-type equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 211 (2022) no. 1, pp. 48-64. http://geodesic.mathdoc.fr/item/TMF_2022_211_1_a3/