Geodesic
Generalized Darboux transformation for the~discrete Kadomtsev--Petviashvili equation with self-consistent sources
Teoretičeskaâ i matematičeskaâ fizika, Tome 196 (2018) no. 3, pp. 434-448

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We construct several types of Darboux transformations for the discrete Kadomtsev–Petviashvili equation with self-consistent sources (dKPwS) including the elementary Darboux transformation, the adjoint Darboux transformation, and the binary Darboux transformation. These Darboux transformations can be used to obtain some solutions of the dKPwS. We give some solutions explicitly.
Keywords: integrable system with self-consistent sources, discrete Kadomtsev–Petviashvili equation
Mots-clés : Darboux transformation, Hirota equation, soliton solution. 
@article{TMF_2018_196_3_a5,
     author = {Runliang Lin and Yukun Du},
     title = {Generalized {Darboux} transformation for the~discrete {Kadomtsev--Petviashvili} equation with self-consistent sources},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {434--448},
     publisher = {mathdoc},
     volume = {196},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_196_3_a5/}
}
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Runliang Lin; Yukun Du. Generalized Darboux transformation for the~discrete Kadomtsev--Petviashvili equation with self-consistent sources. Teoretičeskaâ i matematičeskaâ fizika, Tome 196 (2018) no. 3, pp. 434-448. http://geodesic.mathdoc.fr/item/TMF_2018_196_3_a5/