Geodesic
B\"{a}cklund transformation and applications for the~Vakhnenko equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 210 (2022) no. 2, pp. 199-212

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TMF_2022_210_2_a1,
     author = {Min Xue and Hui Mao},
     title = {B\"{a}cklund transformation and applications for {the~Vakhnenko} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {199--212},
     publisher = {mathdoc},
     volume = {210},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2022_210_2_a1/}
}
TY  - JOUR
AU  - Min Xue
AU  - Hui Mao
TI  - B\"{a}cklund transformation and applications for the~Vakhnenko equation
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2022
SP  - 199
EP  - 212
VL  - 210
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2022_210_2_a1/
LA  - ru
ID  - TMF_2022_210_2_a1
ER  - 
%0 Journal Article
%A Min Xue
%A Hui Mao
%T B\"{a}cklund transformation and applications for the~Vakhnenko equation
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2022
%P 199-212
%V 210
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2022_210_2_a1/
%G ru
%F TMF_2022_210_2_a1
Min Xue; Hui Mao. B\"{a}cklund 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/