Geodesic
Cauchy matrix approach to the~noncommutative Kadomtsev--Petviashvili equation with self-consistent sources
Teoretičeskaâ i matematičeskaâ fizika, Tome 213 (2022) no. 3, pp. 437-449

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We develop a direct method, the Cauchy matrix approach, to construct matrix solutions of noncommutative soliton equations. This approach is based on the Sylvester equation, and solutions can be presented without using quasideterminants. The matrix Kadomtsev–Petviashvili equation with self-consistent sources is employed as an example to demonstrate the approach. As a reduction, explicit solutions of the matrix Mel'nikov model for long–short wave interaction are obtained.
Keywords: self-consistent source, noncommutativity, Mel'nikov model, Cauchy matrix approach, integrable system. 
@article{TMF_2022_213_3_a2,
     author = {Zhihao Shi and Shangshuai Li and Da-jun Zhang},
     title = {Cauchy matrix approach to the~noncommutative {Kadomtsev--Petviashvili} equation with self-consistent sources},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {437--449},
     publisher = {mathdoc},
     volume = {213},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2022_213_3_a2/}
}
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Zhihao Shi; Shangshuai Li; Da-jun Zhang. Cauchy matrix approach to the~noncommutative Kadomtsev--Petviashvili equation with self-consistent sources. Teoretičeskaâ i matematičeskaâ fizika, Tome 213 (2022) no. 3, pp. 437-449. http://geodesic.mathdoc.fr/item/TMF_2022_213_3_a2/