Geodesic
B\"acklund transformations for the~Degasperis--Procesi equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 203 (2020) no. 3, pp. 365-379

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We consider the Bäcklund transformation for the Degasperis–Procesi (DP) equation. Using the reciprocal transformation and the associated DP equation, we construct the Bäcklund transformation for the DP equation involving both dependent and independent variables. We also obtain the corresponding nonlinear superposition, which we use together with the Bäcklund transformation to derive some soliton solutions of the DP equation.
Keywords: Degasperis–Procesi equation, Bäcklund transformation, nonlinear superposition formula
Mots-clés : soliton. 
@article{TMF_2020_203_3_a3,
     author = {Hui Mao and Gaihua Wang},
     title = {B\"acklund transformations for {the~Degasperis--Procesi} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {365--379},
     publisher = {mathdoc},
     volume = {203},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2020_203_3_a3/}
}
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Hui Mao; Gaihua Wang. B\"acklund transformations for the~Degasperis--Procesi equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 203 (2020) no. 3, pp. 365-379. http://geodesic.mathdoc.fr/item/TMF_2020_203_3_a3/