Geodesic
Obtaining multisoliton solutions of the~$(2+1)$-dimensional Camassa--Holm system using Darboux transformations
Teoretičeskaâ i matematičeskaâ fizika, Tome 205 (2020) no. 3, pp. 451-466

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We construct and study Darboux transformations for the $(2+1)$-dimensional Camassa–Holm system. We apply a reciprocal transformation that relates the $(2+1)$-dimensional Camassa–Holm system and the linear system associated with the modified Kadomtsev–Petviashvili hierarchy. Using three Darboux transformation operators, we obtain three types of solutions for the $(2+1)$-dimensional Camassa–Holm system, of which one is a multisoliton solution. In addition, we briefly discuss rational solutions.
Keywords: $(2+1)$-dimensional Camassa–Holm system, reciprocal transformation
Mots-clés : Darboux transformation, soliton solution. 
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     author = {Hui Mao},
     title = {Obtaining multisoliton solutions of the~$(2+1)$-dimensional {Camassa--Holm} system using {Darboux} transformations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {451--466},
     publisher = {mathdoc},
     volume = {205},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2020_205_3_a5/}
}
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Hui Mao. Obtaining multisoliton solutions of the~$(2+1)$-dimensional Camassa--Holm system using Darboux transformations. Teoretičeskaâ i matematičeskaâ fizika, Tome 205 (2020) no. 3, pp. 451-466. http://geodesic.mathdoc.fr/item/TMF_2020_205_3_a5/