Geodesic
Bäcklund transformation and applications for the Vakhnenko equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 210 (2022) no. 2, pp. 199-212 Cet article a éte moissonné depuis la source Math-Net.Ru

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With the aid of the reciprocal transformation and the associated Vakhnenko equation, we construct and study a Bäcklund transformation (BT) involving both independent and dependent variables for the Vakhnenko equation. We derive the corresponding nonlinear superposition formula or $2$-BT and $3$-BT and rewrite them in terms of Pfaffians. We also discuss the representation for the general $N$-BT. As applications, some explicit solutions of the Vakhnenko equation are presented.
Keywords: Vakhnenko equation, Bäcklund transformation, nonlinear superposition formula
Mots-clés : loop soliton solution. 
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Min Xue; Hui Mao. Bäcklund transformation and applications for the Vakhnenko equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 210 (2022) no. 2, pp. 199-212. http://geodesic.mathdoc.fr/item/TMF_2022_210_2_a1/

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